COLD ATOM CONTROL WITH AN OPTICAL ONE-WAY BARRIER
by
ELIZABETH A. SCHOENE
A DISSERTATION
Presented to the Department of Physics
and the Graduate School of the University of Oregon
in partial fulfillment of the requirements
for the degree of
Doctor of Philosophy
December 2010
ii
“Cold Atom Control with an Optical One-Way Barrier,” a dissertation prepared by
Elizabeth A. Schoene in partial fulfillment of the requirements for the Doctor of
Philosophy degree in the Department of Physics. This dissertation has been approved
and accepted by:
Dr. Hailin Wang, Chair of the Examining Committee
Date
Committee in charge: Dr. Hailin Wang, Chair
Dr. Daniel A. Steck, Research Advisor
Dr. Jens U. No¨ckel
Dr. David M. Strom
Dr. Jeffrey A. Cina
Accepted by:
Dean of the Graduate School
iii
An Abstract of the Dissertation of
Elizabeth A. Schoene for the degree of Doctor of Philosophy
in the Department of Physics to be taken December 2010
Title: COLD ATOM CONTROL WITH AN OPTICAL ONE-WAY
BARRIER
Approved:
Dr. Daniel A. Steck
The research presented in this dissertation aims to contribute to the field of atom
optics via the implementation and demonstration of an all-optical one-way barrier
for 87Rb atoms—a novel tool for controlling atomic motion. This barrier—a type of
atomic turnstile—transmits atoms traveling in one direction but hinders their passage
in the other direction. We create the barrier with two laser beams, generating its
unidirectional behavior by exploiting the two hyperfine ground states of 87Rb. In
particular, we judiciously choose the frequency of one beam to present a potential
well to atoms in one ground state (the transmitting state) and a potential barrier to
atoms in the other state (the reflecting state). The second beam optically pumps the
atoms from the transmitting state to the reflecting state.
iv
A significant component of the experimental work presented here involves genera-
ting ultra-cold rubidium atoms for demonstrating the one-way barrier. To this end, we
have designed and constructed a sophisticated 87Rb cooling and trapping apparatus.
This apparatus comprises an extensive ultra-high vacuum system, four home-built,
frequency-stabilized diode laser systems, a high-power Yb:fiber laser, a multitude of
supporting optics, and substantial timing and control electronics. This system allows
us to cool and trap rubidium atoms at a temperature of about 30 µK.
The results presented in this dissertation are summarized as follows. We success-
fully implemented a one-way barrier for neutral atoms and demonstrated its asymmet-
ric nature. We used this new tool to compress the phase-space volume of an atomic
sample and examined its significance as a physical realization of Maxwell’s demon.
We also demonstrated the robustness of the barrier’s functionality to variations in
several important experimental parameters. Lastly, we demonstrated the barrier’s
ability to cool an atomic sample, substantiating its potential application as a new
cooling tool.
This dissertation includes previously published coauthored material.
vCURRICULUM VITAE
NAME OF AUTHOR: Elizabeth A. Schoene
GRADUATE AND UNDERGRADUATE SCHOOLS ATTENDED:
University of Oregon, Eugene, Oregon
Harvey Mudd College, Claremont, CA
DEGREES AWARDED:
Doctor of Philosophy in Physics, 2010, University of Oregon
Bachelor of Science in Physics, 2001, Harvey Mudd College
PROFESSIONAL EXPERIENCE:
Graduate Research Fellow, Department of Physics, University of
Oregon, Eugene, Oregon, 6/04—6/08, 9/10—12/10
National Science Foundation GK-12 Fellowship, University of Oregon,
Eugene, Oregon, 6/08—6/10
Graduate Teaching Fellow, University of Oregon, Eugene, Oregon,
9/03—6/04
Peace Corps Volunteer, United States Peace Corps, Georgetown,
Guyana, 6/01—8/03
vi
GRANTS, AWARDS AND HONORS:
National Science Foundation GK-12 Fellowship, The University of
Oregon, 6/08—6/10.
Outstanding Summer Research Presentation Award, The University of
Oregon, 9/04.
Summer Undergraduate Research Fellowship (SURF), California
Institute of Technology, 6/00—8/00.
Research Experience for Undergraduates (REU), Harvey Mudd College,
5/99—8/99.
PUBLICATIONS:
Elizabeth A. Schoene, Jeremy J. Thorn, and Daniel A. Steck, “Cooling
Atoms with a Moving One-Way Barrier,” Physical Review A 82,
023419 (2010).
Jeremy J. Thorn, Elizabeth A. Schoene, Tao Li, and Daniel A. Steck
“Dynamics of Cold Atoms Crossing a One-Way Barrier,” Physical
Review A 79, 063402 (2009).
Jeremy J. Thorn, Elizabeth A. Schoene, Tao Li, and Daniel A. Steck,
“Experimental Realization of an Optical One-Way Barrier for
Neutral Atoms,” Physical Review Letters 100, 240407 (2008).
J. L. Hardwick, Z. T. Martin, E. A. Schoene, V. Tyng, E. N. Wolf,
“Diode Laser Absorption Spectrum of Cold Bands of C2HD at 6500
cm−1,” Journal of Molecular Spectroscopy 239, 208 (2006).
vii
ACKNOWLEDGEMENTS
I would like to take a moment to recognize many of the people whose support over
the past seven years has been integral to my success, and without which, I probably
would not have survived to write this.
First and foremost, I want to thank my advisor, Dan Steck. Under his calm and
insightful guidance, I learned more than I had imagined possible, from machining
and building circuitry to computer modeling and quantum measurement theory. His
sheer breadth of knowledge and quiet confidence when pursing even the most difficult
problems continues to amaze and inspire me.
I also owe a big thanks to all the members of the Steck Lab, past and present,
including Tao Li, Jeremy Thorn, Peter Gaskell, Aaron Webster, Matthias Fuchs, Eryn
Cook, Jonathan Mackrory, and Paul Martin. They made our lab not just a place to
work, but defined a community and a culture. From friday night LN2 ice cream to a
lab ski trip, there was always some play to balance the work. In particular, I want to
thank my partners in crime, Jeremy Thorn and Tao Li. The three of us built up the
lab from day one, and I owe a huge part of my success to their hard work and help on
the experiment, not to mention the occasional prank and morning discussions about
Laker basketball.
viii
Outside of the lab, I want to thank Patty Smith, Bonnie Grimm, and Brandy
Todd for helping with all the little, hidden things that are so important yet easy to
overlook, in addition to their friendship and encouragement.
I am also extremely grateful for my friendships with Emelie Harstad, Elsa Johnson,
and Kathy Hadley, who provided unwavering support during some of my roughest
times, keeping me safe and sane, not to mention physically fit.
The GTFF requires some thanks as well, for providing an escape from the physics
department and infusing my graduate work with union activism. My GTFF friends
Lisa Hamilton, Glenn Morris, and Jessalynn Strauss also deserve a heartfelt thanks
for their encouragement, support, and non-physics perspective on matters.
I owe a special thanks to my land lord and friend, Karen Martin. She welcomed
Pluto and I into her home, offered friendship, guidance, and dog sitting assistance,
and never seemed to tire of me, Pluto, or his antics.
I am also immensely grateful to my Dad, Clare, and Katura for their love, patience,
and faith in me throughout the years. I am especially thankful for their willingness
to put aside their busy lives to talk on the phone with me when I needed support. I
also want to thank my cousin, Lynne, for so generously “adopting” me into her family
since I moved to Oregon.
And lastly, I must thank my dog Pluto, who has managed to simultaneously inject
stability and insanity (not to mention sheer cuteness) into my life that has helped me
push through the hard times and celebrate the good times.
ix
To Poppy, who quietly supported me over the past seven years, and to whom I
am the most proud to say “I have finished.”
xTABLE OF CONTENTS
Chapter Page
I. AN INTRODUCTION TO ATOM OPTICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2. Important Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3. Light Forces on Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4. Cooling with Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5. Magneto-Optical Trapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.6. The Optical Dipole Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.7. Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.8. Phase Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
II. EXPERIMENTAL SETUP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3. Laser System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.1. Slave Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.2. Master Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.3. Locking the Slave to the Master . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3.4. Acousto-Optic Modulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3.5. Frequency Locking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.3.6. Saturated-Absorption Spectroscopy Setup . . . . . . . . . . . . . . . . . . . . . . . 36
2.3.7. Fibers and Fiber Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3.8. Optical Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.4. Vacuum Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.4.1. High-Pressure Side. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.4.2. Low-Pressure Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.4.3. Vacuum Chamber Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
xi
Chapter Page
2.4.4. Baking Out the Vacuum Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.5. The Dipole-Trap Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2.6. Imaging System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.7. Control and Timing Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
III. THE ONE-WAY BARRIER PART I: THE MECHANICS . . . . . . . . . . . . . . . . 72
3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.2. How It Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.3. Maxwell’s Demon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.4. Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.5. Optical Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.6. The Separation of the Barrier Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.7. Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
IV. THE ONE-WAY BARRIER PART II: DEMONSTRATION AND
CHARACTERIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.2. The Dipole Trap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.3. Demonstrating the One-Way Barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.4. Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.5. A Maxwell’s Demon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.6. The Robustness of the Barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.6.1. The Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.6.2. The Loading Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.6.3. The Repumping-Barrier-Beam Power . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.6.4. The Main-Barrier-Beam Detuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
V. COOLING WITH THE ONE-WAY BARRIER . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.2. How It Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.3. Experimental Setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
xii
Chapter Page
5.4. Demonstrating Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.5. Effect of Translation Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.6. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5.7. Anomalous Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
VI. CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
xiii
LIST OF FIGURES
Figure Page
1.1. Schematic diagram showing some important features of an optical
dipole trap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1. Schematic diagram and pictures of the slave laser. . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2. Schematic of the optical elements used to control and shape the
diode laser’s output beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3. Schematic diagram and picture of the master laser. . . . . . . . . . . . . . . . . . . . . . . . 29
2.4. Hyperfine structure for the 87Rb D2 transition. . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.5. The optical setup for double-passing an acousto-optic modulator. . . . . . . . . . 34
2.6. The saturated-absorption spectrum for the 87Rb F = 2 → F ′
hyperfine transition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.7. Schematic of the of the optical layout for saturated-absorption
spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.8. Schematic of the basic optical setup for producing the MOT-
trapping and repump light. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.9. Picture of the fixture for coupling the fiber attached to a mirror mount. . . . 42
2.10. Picture of the optical table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.11. The high-pressure side of the chamber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.12. Schematic diagram of the rubidium source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.13. The different components connected to the spherical square. . . . . . . . . . . . . . . 48
2.14. The x, y, and z Helmholtz-coil-pair specifications for the pyramid
MOT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.15. Schematic diagram of the low-pressure side of the chamber viewed
from the top. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.16. Picture of the CF cross mounted on the spherical cube. . . . . . . . . . . . . . . . . . . . 52
2.17. Schematic diagram of the low-pressure side of the chamber viewed
from the side. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.18. Pictures showing the assembly of our home-built vacuum cell. . . . . . . . . . . . . . 55
2.19. Schematic diagram showing the cross-section of the Hellma cell
mounting apparatus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.20. Picture of the Hellma cell mounted using the modified 2.75′′ and
4.5′′ CF flanges with the lead-alloy gaskets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.21. The x, y, and z Helmholtz-coil-pair specifications for the second MOT. . . . . 59
xiv
Figure Page
2.22. Pictures of three of the more stunning vacuum components after
baking for 48 hours at 480◦C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.23. Picture of the partially-constructed oven made of vacuum-foil-
covered fire bricks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.24. Picture of the home-built, fiber-laser control box. . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.25. Schematic diagram showing the alignment of the dipole-trap
beam with the MOT and the dumping mirrors. . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.26. Schematic diagram showing the orientation of the CCD camera
and absorption-imaging beam relative to the dipole trap. . . . . . . . . . . . . . . . . . 68
2.27. Schematic diagram of the absorption-imaging optics. . . . . . . . . . . . . . . . . . . . . . . 70
3.1. Energy level structure for the three-level atom. . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.2. Schematic diagram illustrating different aspects of the one-way barrier. . . . . 75
3.3. Illustration of the one-way barrier compressing the volume of a
sample of gas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.4. Hyperfine structure for the 87Rb D2 transition showing the relevant
laser frequencies for the main barrier beam and the repumping
barrier beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.5. Saturated-absorption spectrum for the rubidium D2 transition
showing the relative frequencies for the 85Rb and 87Rb isotopes. . . . . . . . . . . . 83
3.6. Schematic diagram illustrating the orientation of the barrier
beams relative to the dipole-trap axis and focus. . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.7. Optical potentials experienced by the atoms along the dipole-
trap axis due to the dipole-trap beam and the main barrier beam.. . . . . . . . . 84
3.8. Optical layout for producing and controlling the geometry of
the barrier beams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.9. Illustration of the mirror mount knob used to control the barrier
beam separation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.10. Depiction of the typical vertical shifts we observed on the petcam
for the relative height of the main barrier beam and repumping
barrier beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.11. Schematic diagram showing the orientation of the x, y, and z
alignment dimensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.12. Illustration of the reflection-based alignment technique for overlapping
the dipole-trap focus with the blue-detuned barrier-beam focus. . . . . . . . . . . . 95
3.13. Images demonstrating the horizontal (x-direction) alignment
concept for intersecting the blue-detuned barrier-beam focus
with the dipole-trap focus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.1. Diagram showing the orientation of the x-, y-, and z-dimensions
relative to the dipole-trap-beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
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Figure Page
4.2. Image sequence showing the atomic cloud oscillating about the
center of the dipole trap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.3. Illustration of the one-way barrier demonstration procedure. . . . . . . . . . . . . 103
4.4. Schematic diagram showing the optical arrangement identifying
the transmitting and reflecting sides of the one-way barrier. . . . . . . . . . . . . . 104
4.5. Atomic distributions in the dipole trap interacting with the barrier. . . . . . 105
4.6. Populations on the left- and right-hand sides of the barrier as
function of time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.7. Measured and simulated populations on the left- and right-hand
sides of the barrier up to 2 seconds after initially loading the
trap full of atoms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.8. Populations on the left- and right-hand sides of the barrier as a
function of time for atoms loaded to fill the entire trap. . . . . . . . . . . . . . . . . . 114
4.9. Populations on the left- and right-hand sides of the barrier as a
function of barrier-beam separation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.10. Populations on the left- and right-hand sides of the barrier as a
function of loading position. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.11. Populations on the left- and right-hand sides of the barrier as a
function of time for several different loading positions. . . . . . . . . . . . . . . . . . . 122
4.12. Populations on the left- and right-hand sides of the barrier as a
function of repumping-barrier-beam power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.13. Populations on the left- and right-hand sides of the barrier as a
function of time for different repumping-barrier-beam powers. . . . . . . . . . . . 126
4.14. A schematic showing the 87Rb D2 emission spectrum and the
three detunings used to test the reflectivity of the barrier. . . . . . . . . . . . . . . . 128
4.15. Populations on the right- and left-hand sides of the trap as a
function of time for three different main-barrier-beam detunings. . . . . . . . . 129
5.1. Illustration of how to use the one-way barrier to cool a sample of gas. . . . 134
5.2. Schematic representation of the one-way-barrier cooling process
for a gas confined in a harmonic potential. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
5.3. Schematic diagram showing the alignment of the dipole-trap
beam with the MOT and the dumping mirrors for the one-way-
barrier cooling experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.4. Illustration of the dipole-trap translation and imaging sequence. . . . . . . . . 142
5.5. Atomic distributions in the dipole trap during translation with
and without the one-way barrier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.6. The FWHM of the spatial distribution in the dipole trap as a
function of time during the translation with and without the
one-way barrier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
xvi
Figure Page
5.7. The width of the atomic distribution in the dipole trap as a
function of translation velocity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
5.8. The width of the atomic distribution in the dipole trap with
and without the one-way barrier for several seconds after the
sweep has finished. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
5.9. The width of the atomic distribution after completing one and
two sweeps through the barrier as a function of time. . . . . . . . . . . . . . . . . . . . 152
5.10. The power reaching a photodiode as the air cart comes to rest,
partially blocking a laser beam with an attached razor blade. . . . . . . . . . . . 155
5.11. The center position of the atomic distribution in the dipole trap
after the air cart has come to rest as a function of time. . . . . . . . . . . . . . . . . 156
5.12. The width of the atomic distribution after the air cart has come
to rest as a function of time for an acceleration of 100 and
500 mm/s2 and a velocity of 5 mm/s.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
5.13. The width of the atomic distribution as a function of time for
atoms loaded into the center of the trap with no barrier or air-
cart movement and for atoms swept through the barrier once. . . . . . . . . . . . 158
5.14. The width of the atomic distribution as a function of time for
atoms loaded into the center of the trap for the nine combinations
of 10, 15, and 19 W dipole-trap loading powers and 10, 15, and
19 W dipole-trap operating powers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
1CHAPTER I
AN INTRODUCTION TO ATOM OPTICS
1.1. Introduction
The idea that light can affect the motion of atoms by exerting a pressure was first
described mathematically by Maxwell in 1873 [1], then later verified experimentally
near the turn of the century [2–5]. However, it was only in the late 1970’s that
researchers started to develop schemes that harnessed these effects for useful purposes,
such as cooling and trapping ions and neutral atoms [6–9]. These efforts gave birth to
the field of atom optics, whose main thrust is the control and manipulation of atomic
motion with laser light. This new field progressed rapidly, garnering widespread
attention for the development of a relatively simple, yet robust technique for cooling
atoms to microKelvin temperatures [10–12], and culminated in the achievement of
dilute-gas Bose-Einstein condensation [13–15]—a new state of matter predicted by
Einstein and Bose 70 years earlier that flirts with the limits of absolute zero.
Atomic cooling and motional control constitute the dual pursuits of atom-optics
research, and both areas boast a myriad of notable achievements. During the late
1980’s, atomic cooling schemes proliferated due to the quest for ever lower tempera-
tures. Techniques incorporating polarization gradient cooling [16, 17] routinely came
2within an order of magnitude of the recoil limit (∼ 0.2 − 2 µK depending on the
atom), which corresponds to the kinetic energy imparted to an atom due to the
recoil from emitting one photon. Two more schemes—appropriately dubbed “sub-
recoil cooling” techniques—pushed temperatures below the recoil limit [18, 19], with
one experiment reaching a temperature of 180 nK [20]. Achievements in controlling
atomic motion paralleled the success of the cooling methods, as cold atoms are far
easier to manipulate. This led to such novel constructs as atom gratings [21], lenses
[22, 23], beamsplitters [24, 25] and interferometers [26–29], and drove advancements
in the precision of atomic clocks [30, 31], the field of condensed matter physics via
Bose-Einstein condensation [32] and degenerate Fermi gases [33, 34], and quantum
information processing [35].
Bolstered by this wide array of accomplishments, the field of atom-optics research
continues to thrive, working towards expanding cooling methods to new atomic and
molecular species and probing the limits of atomic control. The work presented in
this dissertation examines an all-optical one-way barrier for atoms—a type of atomic
turnstile—which allows atoms to transmit when traveling in one direction, but inhibits
their passage in the other direction. This work contributes to the coupled objectives
of atom optics—cooling and control—as we demonstrate its ability to both direct
atomic motion and reduce the temperature of an atomic sample.
31.2. Important Concepts
The notion that light can influence the center-of-mass motion of an atom should
not come as a surprise, since absorption or emission of a photon necessitates a change
in the atom’s momentum due to the recoil from the event. We also know from
classical mechanics that changes in momentum result from forces acting on a system,
so that light must exert a force on the atom, even during an interaction with a single
photon. Understanding the nature of these forces was crucial to the development of
the multitude of clever techniques and applications that define the field of atom optics,
and the pertinent physics is well documented in a number of references [9, 36, 37].
Having said that, we will briefly cover some of the important concepts particularly
relevant to the work presented in this dissertation and refer the reader to the references
for a more comprehensive discussion.
1.3. Light Forces on Atoms
In this section we will examine a two-level atom using a semi-classical approach,
where we treat the atom quantum mechanically and the light field classically. Addi-
tionally, we will assume that the light field is monochromatic, and restrict the dis-
cussion to motion in one dimension (the z-direction) for simplicity, where z will refer
to the mean atomic position. During this discussion we will draw on well established
quantum optics methods and results, such as use of the rotating wave approximation,
the rotating frame, and solutions of the optical Bloch equations [37–39].
4Just as in classical mechanics, the force exerted on an atom is given by its change
in momentum,
Fˆatom =
dpˆ
dt
, (1.1)
though here the force and momentum are quantum mechanical operators in the
Heisenberg picture, such that they contain the time dependence. In this picture,
the equation of motion for an operator Aˆ is given by
dAˆ
dt
=
i
~
[Hˆ, Aˆ], (1.2)
where Hˆ is the Hamiltonian. Evaluating the commutator using the relationship
pˆ = −i~ ∂
∂z
, (1.3)
yields the expression for the force
Fˆatom = −∂Hˆ
∂z
. (1.4)
For our purposes, Hˆ = HˆI is the Hamiltonian that describes the atom-field
interaction, and is given by the expression
HˆI =
~
2
(
Ω∗(z)σˆ + Ω(z)σˆ†
)
, (1.5)
in the rotating frame, which removes the explicit eiωt time dependence of the light
field. Here, σˆ = |g〉〈e| and σˆ† = |e〉〈g| are the atomic lowering and raising operators,
respectively, while Ω(z) is the position-dependent Rabi frequency [37], given by
Ω(z) = |Ω(z)|eiφ(z), (1.6)
5where
|Ω(z)| = −2
~
〈g|εˆ · d|e〉|E0(z)|. (1.7)
The term 〈g|εˆ · d|e〉 is the dipole matrix element and εˆ indicates the polarization
direction of the electric field. The position dependence of the Rabi frequency reflects
the fact that the amplitude and phase of the light-field (|E0(z)|eiφ(z)) can vary spa-
tially.
Taking the spatial derivative of the interaction Hamiltonian and then using 〈Aˆ〉 =
Tr[ρˆAˆ] to find the expectation value produces the expression for the mean force
〈Fatom〉 = −~
2
Ω∗(z)
(
∂z|Ω(z)|
|Ω(z)| − i∂zφ(z)
)
ρ˜eg(z) + c.c. (1.8)
Here, we replaced the expectation value for the lowering operator 〈σˆ〉 by the position
dependent optical coherence, ρ˜eg(z), given by the off-diagonal matrix elements of
the interaction Hamiltonian. For stationary or slowly moving atoms (slowly moving
compared to their decay time), we can use the expression for the coherence from the
steady-state solution of the optical Bloch equations, which is given by
ρ˜eg(z) =
−iΩ(z)(Γ/2 + i∆)
|Ω(z)|2 . (1.9)
Here, Γ is the atomic decay rate and ∆ = ω − ω0 is the detuning, defined as the
difference between the atomic transition frequency ω0 and the frequency of the light
field ω. Substituting this expression into the equation for the mean force yields
〈Fatom〉 = ~|Ω(z)|
2
2
(
Γ2/4 + ∆2
)
+ |Ω(z)|2
(
Γ
2
∂zφ(z)−∆∂z|Ω(z)||Ω(z)|
)
. (1.10)
6The expression for the force has two distinct terms that produce fundamentally
different types of forces. We note that the first term is proportional to the decay rate,
Γ, and results from the light field’s phase dependence on position. This force is called
the “radiation pressure force,” and arises from momentum changes due to absorption
and spontaneous emission of light. The dependence on spontaneous emission renders
this force dissipative, as spontaneous emission is an irreversible process, and gives
it a central role in many cooling schemes. The second term, on the other hand, is
proportional to the detuning of the light, and results from the spatial variation of the
optical intensity. This force is referred to as the “dipole force,” and to the lowest order
in |Ω|/∆, originates from shifts in the atomic energy levels due to the electric field of
the light. In contrast to the radiation pressure force, the dipole force is conservative,
which makes it impractical for cooling atoms but rather a major player in optical
trapping techniques. We will examine the dipole force more closely in Section 1.6.
1.4. Cooling with Light
To understand how to use the force of light on an atom to slow its motion, we must
consider how velocity enters into the force calculations. An exact solution involves
solving the optical Bloch equations including the mean atomic velocity, though this
produces differential equations that are difficult to solve. A simpler approach treats
the velocity as a perturbation to the position dependent parameters (i.e. Ω(z), ρ˜eg(z),
etc.) and keeps only the first-order terms [36]. The resulting expression for the force
7on an atom is quite complicated, so we will focus on the particular case of a plane
wave.
For a plane wave of the form
E(z, t) = εˆ
E0
2
(
ei(kz−ωt) + e−i(kz−ωt)
)
, (1.11)
the mean force on an atom is given by
〈Fatom〉 = ~k Γ Ω
2
0
4
(
∆2 + Γ2/4 + Ω 20 /2
)(1 + 2∆(k · v)(
∆2 + Γ2/4 + Ω 20 /2
)). (1.12)
Here, Ω0 is the regular, real Rabi frequency
Ω0 = −〈g|εˆ · d|e〉|E0|~ , (1.13)
with no position dependence nor complex components, and v is the velocity vector
for the atom. The first term is the velocity-independent force on a stationary atom
in a plane wave, which is given by the scattering rate multiplied by the momentum
recoil per photon, ~k. The second term gives the velocity-dependent part of the force,
where we see that the magnitude of the force is proportional to the velocity. We also
observe that the direction of the velocity-dependent force always opposes the atom’s
motion when ∆ < 0 (red-detuned light). For two counter-propagating plane waves,
this feature results in a damping force that slows the atomic motion for red-detuned
light. We can see this by recognizing that in the low intensity limit—when stimulated
emission is negligible—the total force on an atom is given by the sum of the force for
each plane wave [36]. The sum cancels out the velocity-independent term (due to the
opposite k vectors), but leaves the damping part intact.
8We can understand the origin of the damping force by considering the Doppler
shift of an atom moving in the two counter-propagating plane waves for ∆ < 0. In
particular, the plane wave directed opposite the atom’s motion is Doppler shifted
slightly closer to the atomic resonance, such that the atom scatters more light from
this field than the co-propagating one, thus reducing its velocity. This cooling
technique is appropriately called “Doppler cooling” due to its dependence on the
Doppler shift, and is referred to as “optical molasses” [40] when implemented in three
dimensions, as it is highly effective at rapidly cooling an atomic sample to microKelvin
temperatures. Wineland et al. [41] provides a nice tutorial on the concepts behind
Doppler cooling. The standard, experimental realization of optical molasses involves
three, opposed pairs of laser beams, one for each dimension.
1.5. Magneto-Optical Trapping
Though enormously successful at cooling atoms, optical molasses has no ability
to trap them by constraining their position. Consequently, nothing prevents the
atoms from diffusing out of the cooling beams, and hence, the region of experimental
interest. The cooling utility of optical molasses stems from the velocity dependence of
the detuning for a moving atom, which results in the atom scattering more light from
the opposing field. A similar approach can be implemented to trap the atom as well
by making the detuning position-dependent. In this case, the atom will scatter more
9light from the opposing field when it is displaced from a specified origin, pushing it
back towards that position.
We can make the detuning position-dependent by adding a magnetic field that
changes linearly with position. An atom moving in this magnetic field will experience
a position-dependent Zeeman shift of its energy levels, which effectively alters the
detuning of the light and thus the scattering rate, depending on the atom’s position
relative to the zero of the magnetic field. Circularly polarized light is required to
create asymmetric scattering rates for the two counter-propagating plane waves.
We can incorporate the effect of the magnetic field into the force calculation by
including the Hamiltonian that describes the Zeeman shift [42]
HˆZ = −µˆ ·B (1.14)
into the interaction Hamiltonian HˆI. Here, µˆ is the magnetic moment operator for
the atom and B = B0z, where z is the atomic position vector. For an atom moving in
two counter-propagating plane waves with opposite circular polarizations, this yields
(to the lowest order in v and z) [36]
〈Fatom〉 = ~k Γ Ω
2
0 ∆(
∆2 + Γ2/4 + Ω 20 /2
)2
(
k · v + µ
′B0
~k
k · z
)
, (1.15)
where µ′ is the effective magnetic moment for the transition [36]. Similar to the
velocity-dependent force, we see that the position-dependent force always pushes the
atom in the direction opposite its position vector for ∆ < 0, driving the atom toward
the zero of the magnetic field.
10
Implementing optical molasses in tandem with a three-dimensional, linear mag-
netic field creates a powerful cooling and trapping tool called a “magneto-optical
trap” (MOT) [43]. The MOT has become by far the most prolific atomic cooling
and trapping technique due to its relatively straightforward implementation and
robustness to significant variations in the different experimental parameters. As such,
it serves as the starting point for nearly all atom-optics experiments, as it does for the
one-way barrier experiments discussed in this dissertation. References [10–12, 36, 44]
have nice discussions on the concepts and mechanics of a MOT, which we did not
cover in great detail here.
1.6. The Optical Dipole Force
The origin of the optical-dipole force discussed in Section 1.3 can be traced to
the ground- and excited-state coherences generated by the atom-field interaction.
To understand this, we will examine the atom-field Hamiltonian under the same
idealizations outlined previously (two-level atom, monochromatic field, etc.), high-
lighting a few salient features.
The atom-field Hamiltonian HˆAF in the rotating frame is given by the sum of the
atomic and interaction Hamiltonians
HˆAF = Hˆatom + HˆI (1.16)
HˆAF = −~∆ σˆ†σˆ + ~Ω0
2
(
σˆ† + σˆ), (1.17)
where we have not included any position dependence in the Rabi frequency Ω0. This
11
Hamiltonian can be represented in the atomic-state basis (the |e〉 and |g〉 basis) by
the matrix
HˆAF →
 0 ~Ω02~Ω0
2
−~∆
 , (1.18)
where the presence of off-diagonal matrix elements, which describe the ground- and
excited-state coherences, indicate that the atomic energy levels are not eigenvalues of
this Hamiltonian. We can diagonalize this matrix to find the new eigenstates, which
have eigenvalues
E± = −~∆
2
± ~
2
√
∆2 + Ω 20 , (1.19)
that shift the atomic ground- and excited-state energy levels from their non-inter-
acting values. We can see from this expression that the optical coherences are
responsible for the energy shifts, which are called “ac Stark shifts” since they originate
from the oscillating (ac) electric field. Of particular importance is the case when the
detuning is large (|∆|  |Ω0|,Γ) and the interaction is no longer resonant. Under
these circumstances, the atom will remain almost exclusively in the ground state and
the energy shift due to the electric field is approximated by the expression
∆Eg ≈ ~Ω
2
0
4 ∆
. (1.20)
Since Ω 20 is proportional to the field intensity, we see that the magnitude of the energy
shift depends on both the detuning and the intensity of the field, while the direction of
the shift depends on the sign of the detuning. It is not hard to see that if the intensity
12
of the field varies with position, such as for a focused laser beam, the magnitude of
the energy shift will become position-dependent.
In this case, a conservative force must accompany the change in energy an atom
experiences as it moves through the intensity gradient of the light field, since no
energy is dissipated in the process (e.g. from spontaneous emission). This allows us
to write the mean force as the negative gradient of a potential
〈Fdipole〉 = −∂zVdipole, (1.21)
expressed here for a one-dimensional potential. In fact, we can rearrange the dipole
term in the equation for the force of light on an atom [Eq. (1.10)] to fit this form
[37]:
〈Fdipole〉 = −~∆
2
∂zlog
[
1 +
|Ω(z)|2
2
(
Γ2/4 + ∆2
)], (1.22)
where Vdipole is given by
Vdipole =
~∆
2
log
[
1 +
|Ω(z)|2
2
(
Γ2/4 + ∆2
)], (1.23)
and the position dependence is built into the Rabi frequency. In the limit of a large
detuning (|∆|  |Ω(z)|,Γ), we can approximate this force and the corresponding
potential by the expressions
〈Fdipole〉 ≈ − ~
4∆
∂z
(|Ω(z)|2) (1.24)
Vdipole ≈ ~ |Ω(z)|
2
4∆
. (1.25)
13
Here, the expression for the potential replicates the result obtained for the ac Stark
shift in this limit, but with a complex and position-dependent Rabi frequency. An
atom interacting with the light field will navigate the potential energy curve defined
by the field’s intensity profile, with the strength of the potential determined by the
field’s detuning and intensity at any given position. The detuning also controls the
sign of the potential, with red-detuned light (∆ < 0) forming an attractive potential
and blue-detuned light (∆ > 0) creating a repulsive potential.
We also see that the magnitude and direction of the force exerted on the atom
depend on both the magnitude and sign of the intensity gradient and the detuning.
We can illustrate this by considering a focused, Gaussian beam with the longitudinal
intensity profile depicted in Figure 1.1(a). In this situation, the direction of the force
an atom experiences when displaced to the right of the focus (where the force is
zero) depends exclusively on the sign of the detuning, since the intensity profile has a
negative slope at this position [Fig. 1.1(b)]. In particular, red-detuned light produces
a force opposite the atom’s position vector, which pushes it back towards the region
of highest intensity (the focus) [Fig. 1.1(c)]. The sign of the force reverses for blue-
detuned light, such that the atom is repelled from the region of highest intensity.
At first glance, it appears that creating a strong potential simply involves cranking
up the intensity of the field relative to the detuning. While this indeed increases the
potential strength, it also increases the scattering rate, heating the atom and ruining
the conservative nature of the force. Fortunately, the scattering rate is proportional
14
(a) (b)
I
z
z
y
F
za
a
< 0! 
(a)
(b)
(c)
Figure 1.1. Schematic diagram showing some important features of an optical dipole
trap. (a) Geometry of a focused, single-beam optical dipole trap. (b) Intensity profile
along the longitudinal dimension of the trap. (c) Illustration of the force Fa acting
on a trapped atom when displaced from the focus by a distance za for a red-detuned
trap.
to I/∆2 (as opposed to I/∆ for the potential), so very large detunings and intensities
can create strong potentials with minimal scattering.
A wide variety of atom traps exploiting the optical dipole potential for both red-
and blue-detuned light have been implemented over the years [45–47]. These are
collectively referred to as “optical dipole traps,” reflecting the purely optical (e.g.
not magnetic) nature of the confinement. The most simple example of an optical
dipole trap is the focused, single-beam trap mentioned above, which describes the
relevant physics for both applications of this phenomenon used in our experiments.
1.7. Temperature
Laser cooling techniques are powerful experimental tools due to their exceptional
ability to slow atomic motion. The slow atomic speeds correspond to very low mean
15
kinetic energies, which we can relate to a temperature T for a one-dimensional thermal
distribution using the equipartition theorem
〈Ekin〉 = kBT
2
, (1.26)
where k
B
is Boltzmann’s constant. Though an atomic ensemble in atom-optics
experiments may not necessarily be in thermal equilibrium, it is still convenient to
report a temperature to describe the ensemble’s average kinetic energy. As such,
the temperature quickly became an important metric for evaluating and comparing
different slowing schemes, earning them the collective moniker “laser cooling tech-
niques.” Due to the importance of temperature measurements both in atom-optics
research in general and, in particular, to the work presented in this dissertation (where
we demonstrate a new cooling technique), we will outline a few methods for measuring
the temperature and indicate their application in our experiments. We also note that
throughout this section we discuss the temperature for a one-dimensional atomic
distribution, though technically temperature is not defined unless all velocity compo-
nents are considered.
A very common technique for measuring the temperature utilizes the free ex-
pansion of an atomic ensemble, and is referred to as a “time of flight” measurement.
In this technique, an image of the atomic sample’s spatial distribution is taken after
a brief (roughly 10 − 20 ms) period of free expansion. For sufficient expansion
times, the final spatial distribution directly reflects the momentum distribution at
the time of release, as each atom’s momentum determines how far it will travel
16
during the expansion. The momentum distribution is found by converting the spatial
distribution’s position coordinate to momentum using the equation
p =
mx
t
, (1.27)
where m is the atomic mass and t is the expansion time. For a Gaussian momentum
distribution, the temperature is given by the expression [47]
T =
σ 2p
mk
B
, (1.28)
where σp is the width of the momentum distribution. We used this method to measure
the temperature of the atoms in our MOT, though the small diameter of our laser
beams made this method less than desirable for most of our measurements, since the
atoms would rapidly expand out of the beams.
With the exception of measuring the temperature of the magneto-optically trapped
atoms, all our other temperature measurements involved atoms confined in an optical
dipole trap. For these atoms, the (steady-state) spatial density distribution in the
dipole trap is related to the temperature through the expression [47]
n(z) = n0e
(
−U(z)
k
B
T
)
, (1.29)
where U(z) is the one-dimensional trapping potential and n0 is the density at the
zero of the potential. For the focused, single-beam dipole trap employed in our
experiments, we can approximate the potential near the focus (within about a third
of the Rayleigh length) as harmonic. Under these circumstances, the temperature of
17
the atoms directly relates to the width of the Gaussian density distribution σz and
the harmonic trap frequency ωz by the equation
T =
m
k
B
σ 2z ω
2
z . (1.30)
Unfortunately, the spatial extent of our atomic ensemble reaches well beyond the
region appropriate for using the harmonic approximation. In this case, the width of
the distribution still indicates the temperature, however, the dependence is no longer
quadratic.
Though we do not explicitly know how the temperature depends on the spatial
distribution’s width outside the harmonic approximation, we can still calculate the
temperature by making use of the virial theorem,
2〈 [〈Ekin〉] 〉t = −
N∑
k=1
〈Fk · zk〉t , (1.31)
which relates the average kinetic and potential energies of N particles, in equilibrium,
bound by a potential. Here, Fk is the force on the k
th particle at position z due
to the dipole potential, which we have assumed to be one-dimensional, and the
outer angle brackets 〈 〉t denote the time average. We consider the atoms to be in
equilibrium because the spatial distribution does not change much. We can calculate
the temperature from the average kinetic energy using Eq. (1.26).
18
1.8. Phase Space
Generally speaking, the phase space for the one-dimensional motion of a classical
particle describes all the possible position and momentum states (x, p) accessible to
the particle for a given energy. The probability of finding the particle at position x
with momentum p is given by the joint probability distribution ρ(x,p), which is called
the “phase-space density.” For a classical particle, the position and momentum can
be known with arbitrary certainty, such that ρ(x,p) is sharply peaked about those
values. This is not the case, however, for an ensemble of cold atoms, where the exact
position and momentum for individual particles are not known due to their small size
and high density. In this situation, the position and the momentum of the ensemble
become important, and the phase-space density is related to the ensemble’s spatial
and momentum distributions.
A particularly useful quantity when discussing ensembles of cold atoms is the
average phase-space density, defined for one dimension as
〈ρ(x, p)〉 =
∫
ρ 2(x, p)dxdp. (1.32)
We can use the average phase-space density to characterize the extent of the joint
probability distribution in x − p space in terms of the phase-space density ρD and
phase-space volume ρV,
ρD = N〈ρ(x, p)〉 (1.33)
ρV =
N
ρD
, (1.34)
19
where N is the number of atoms in the ensemble. Note that we are using the term
“phase-space density” to describe two different quantities; here we are referring to
an actual density that incorporates the number of particles, whereas previously we
were referring to the joint probability distribution ρ(x,p). We also note that the
terms “phase-space density” and “phase-space volume” are both commonly used in
the literature.
To compute the average phase-space density, we start by assuming the velocity
distribution is independent of position, allowing us to write
ρ(x, p) = ρx(x)ρp(p). (1.35)
Here, ρp(p) is given by the Maxwell-Boltzmann momentum distribution, which links
the average phase-space density to the temperature of the ensemble. This allows us
to evaluate the momentum integral separately, yielding the expression
〈ρ(x, p)〉 = 1√
2pimk
B
T
∫
ρ 2x (x)dx (1.36)
for an arbitrary position distribution. For a Gaussian position distribution, the
expression for the average phase-space density simplifies to
〈ρ(x, p)〉 = 1
σx
√
mk
B
T
, (1.37)
where σ 2x is the variance of the Gaussian position distribution.
When cooling atoms, we typically are not interested in the absolute phase-space
volume, but rather the change in phase-space volume. Colder atoms correspond to
20
smaller phase-space volumes, and the amount of phase-space compression achieved
for a cooling process is regarded as a figure of merit. Though temperature provides
one measure of the effectiveness of a cooling technique, phase-space compression is
a more powerful measure as it speaks to the increase in the density of the atoms as
well. We can calculate the compression factor for a Gaussian position distribution
using the ratio
ρ iV
ρ fV
=
σ ix
√
T i
σ fx
√
T f
, (1.38)
which simplifies to
ρ iV
ρ fV
=
(σ ix)
2
(σ fx )2
(1.39)
by relating the temperature of the Gaussian distribution to its width using Eq. (1.30).
Here, the superscript i indicates the initial value and the superscript f the final value.
Figures 3.7, 4.5, 4.7-4.15, 5.2, and 5.4-5.7 have been published with coauthors.
21
CHAPTER II
EXPERIMENTAL SETUP
2.1. Introduction
The backbone of our one-way barrier experiments is the basic experimental appa-
ratus that enables us to cool and trap 87Rb atoms. Designing and constructing the
appa-ratus constituted a substantial component of realizing these experiments, and
the apparatus will remain functional for future work beyond the one-way barrier.
We devoted part of Chapter 1 to explaining the basic physics of atom cooling and
trapping, and here we will describe the different aspects of implementing those tech-
niques. In particular, we will detail the laser system, ultra-high vacuum system,
magnetic field coils, dipole-trap laser, imaging system, and control and timing elec-
tronics.
2.2. Overview
Our general design employs a double-MOT system [48], where atoms from one
MOT in a higher pressure region of the chamber are rapidly transported to a second
MOT in a lower pressure region. This design traps large numbers of atoms at very
low background pressures. Our particular implementation of the double-MOT system
22
uses a pyramid MOT [49, 50] for the first MOT—which we will describe in more detail
in Section 2.4.1—and the standard, six-beam MOT configuration (Section 1.4, 1.5)
for the second MOT. We use anti-Helmholtz coils to create the linear magnetic field
necessary for trapping (Section 1.5), and pairs of Helmholtz coils to shift the zero-field
position in all three dimensions.
2.3. Laser System
The laser system needed to create a functional magneto-optical trap (MOT) for
87Rb requires two specific, stable laser frequencies—one for the cycling transition and
one for the repump transition (see Section 2.3.5)—adequate power, frequency tuning
capability, µs on/off switching and power control, and the ability to transport the
beams to specific places over long distances. Below we will discuss the various optical
components and techniques we use to fulfill these requirements and form a versatile
laser system.
2.3.1. Slave Lasers
We use two types of home-built diode lasers, but the most basic one is essentially
a free-running (no external feedback) diode that we will refer to as a “slave laser” (see
Section 2.3.3 for the origin of the name). We purchased laser diodes manufactured by
Sharp Micro-electronics (P/N GH0781JA2C) with a nominal wavelength of 784 nm,
a wavelength that is commonly used in CD players, making them fairly cheap and
readily available. This type of laser diode typically has the back facet of the semi-
23
conductor material reflection coated and the front facet anti-reflection (AR) coated,
and the two facets form the cavity necessary for lasing [51]. The beam produced by
this laser diode has a maximum output power of 120 mW, is single mode (transversely
and longitudinally), and in the absence of any optics, the beam is uncollimated, has
an elliptical spatial profile, and is linearly polarized perpendicular to the major axis
of the ellipse [51, 52].
Since the diode is free-running, the temperature of the diode and the current it
receives are the only means to control its power and operating frequency. Typically,
the power output increases linearly with the injection current over threshold [52], and
reducing the temperature increases the output power as well. The dependence of the
frequency on the temperature and the injection current are well documented [51, 52],
showing that generally, warmer diodes and higher injection currents produce longer
wavelengths. It has also been shown that colder diodes tend to have longer life spans
[51].
We secure the diode in a tube with an adjustable lens at the end to collimate the
beam (Thorlabs P/N LT230P-B). We then place this lens tube in an aluminum piece
and hold it in place with a set screw [Fig. 2.1(a)], achieving vertical polarization of the
beam by rotating the lens tube before fixing it in place. We insert two temperature
sensors, a 50 kΩ glass bead thermistor (Fenwall Electronics P/N 121) and an IC
temperature sensor (Analog Devices P/N AD590JH), into the aluminum piece, which
sits on top of a thermo-electric cooler (Melcor P/N CP1.0-127-05L). We sandwich the
24
thermo-electric cooler between the aluminum piece and the aluminum base plate of
the laser housing using nylon screws [Fig. 2.1(c)], ensuring thermal isolation of the
aluminum piece, which is extremely important to help regulate the temperature of
the diode. We feed the electrical connections for the current- and temperature-control
electronics through the base plate and attach them to a small diode protection circuit
board and to the thermo-electric cooler and the temperature sensors, respectively.
We connect the laser diode directlyk to the protection board. The diode, lens tube,
aluminum piece, thermo-electric cooler, and protection circuit are all housed inside a
lid made of polycarbonate, chosen for its low thermal conductivity. The beam exits
the housing through a hole with a microscope slide attached at Brewster’s angle to
prevent back reflections [Fig. 2.1(a)].
After exiting the laser housing we reflect the beam off two steering mirrors and
then pass it through a pre-mounted, anti-reflection coated anamorphic prism pair
(Thorlabs P/N PS875 2.0 X) to correct for the elliptical spatial profile. A half-wave
plate then rotates the beam’s polarization by 45◦ prior to entering an optical isolator
(Conoptics P/N 712B/713A). The isolator guarantees that no back reflections can
reach the diode, and the wave plate ensures the polarization of the light exiting the
isolator is rotated back to vertical, since the isolator rotates it by 45◦ (Fig. 2.2).
The circuitry required to operate this diode laser consists of temperature stabi-
lization and current control electronics. The temperature-control circuit is a basic
proportional, integral, differential (PID) feedback controller built around Wavelength
25
Temperature
Sensors
Nylon 
Screw
Base Plate
Lens 
Tube
Set ScrewLid
Side View
Back View
Base Plate
Thermo-
Electric 
Cooler
Exit Window
Lid Set Screw
Lens 
Tube
Thermo-
Electric 
Cooler
(a)
(c)
(b)
(d)
Figure 2.1. Schematic diagram and pictures of the slave laser. (a) Side view showing
the lens tube, set screw, thermo-electric cooler, base-plate, polycarbonate lid and
Brewster’s angle exit window. (b) Side-view picture of the slave laser. (c) Back view
showing most of the same features plus the temperature sensors and nylon screws.
(d) Front- and top-view picture of the slave laser.
Slave
Laser
Isolator
vapor cell
Anamorphic
Prism Pair
PBSC
f = 500 mm
3/8” window
lens
AOM
R = 500 mm
spherical
mirror
lens
f = 50.2 mm
Differential
Photodiode
mirror 1
Figure 2.2. Schematic of the optical elements used to control and shape the diode
laser’s output beam, including the steering mirrors, anamorphic prism pair, half-wave
plate, and optical isolator.
26
Electronics’ WTC3243 chip, originally designed by Todd Meyrath, then modified for
our appli-cations. The thermo-electric cooler is connected to the control circuit and
it can source or sink heat from the base plate of the laser housing to the aluminum
piece containing the laser diode, depending on the direction of the current flow. The
temperature-feedback measurements are made by the thermistor that is embedded
in the aluminum piece, and the IC temperature sensor (AD590) is connected to a
separate circuit that measures and displays the temperature on an LCD screen (Lascar
Electronics P/N SP-400). The user can adjust the temperature set-point via a 10-
turn potentiometer, and can flip a switch to turn off the feedback control completely.
With these control electronics, the temperature is stable to 3 mK over several days.
The current-controller circuit serves to provide a steady, user-controlled current to
the diode, and also protects the diode from fluctuations and spikes in the power supply.
The steady current supply is accomplished with a PID feedback-control circuit, and
the current output is displayed on an LCD screen. The user can manually adjust
the current with course- and fine-tuning 10-turn potentiometers, and flip a switch
to turn the current to the diode on or off. There is also a current-modulation input
that modifies the current from the value set by the adjustment potentiometers. For
protection, the user can set a current limit that cannot be exceeded by the adjustment
potentiometers or the modulation input. We set the current limit to 110 mA, and a
red LED lights up if the current set-point goes above this value. Additionally, the
diode is automatically shorted when the current turns off for any reason (including
27
power loss), and there is a switch that allows the diode to be shorted even while the
current is on.
2.3.2. Master Lasers
The second type of diode laser we built uses a diffraction grating to feed some of
the laser light back into the diode itself to allow for improved frequency tuning and
to spectrally narrow the output [51]. This type of diode laser is commonly called a
“grating-stabilized diode laser” or a “psuedo-external cavity” diode laser, referring to
the larger cavity formed between the diode’s back facet and the grating. Here we will
refer to it as a “master laser” (see Section 2.3.3 for the origin of the name). Some of
the properties, design, and electronics are the same as for the slave laser described
above, such as the output beam characteristics, the lens tube that holds the diode, the
polycarbonate housing, the Brewster’s angle exit window, the temperature control,
current control, and diode protection electronics, and the series of optics used to align,
shape the beam, and protect against back reflections.
The diffraction grating is arranged in the Littrow configuration [53], where the
zero-order diffraction beam forms the output beam of the laser, while the first-order
diffraction beam is reflected back into the laser diode to provide optical feedback.
The introduction of the grating to form one end of the optical cavity improves the
quality factor of the cavity, and also acts as a frequency selector, since the grating
angle determines the wavelength of light diffracted back into the laser diode. These
improvements narrow the spectral linewidth of the laser and help with frequency
28
control [51]. A nice tutorial and design for a laser in the Littrow configuration is
given by MacAdam [54].
To construct this laser, we used a design by Daniel Steck, Bruce Klappauf, and
Windell Oskay [55–57], which was modified to accommodate 780 nm laser light. This
laser design has also been described in Tao Li’s dissertation [58]. The laser consists
of four pieces, the diode mounting block, the grating mount, and an upper and lower
base plate, all machined from 954 aluminum bronze. This material was chosen for
its strength and fatigue resistance—since two of the laser pieces have thin sections
that are load bearing—as well as its decent thermal conductivity, which helps with
temperature stabilization.
We secure the diode in the mounting block the same way as for the slave laser.
The grating mount allows the grating (Edmund Optics P/N NT43-751) to be glued
onto a lever arm, which is backed by a piezoelectric stack (Noliac P/N SCMA/S2/A/-
5/10/60/9/1500) and a fine-adjustment screw (New Focus P/N 9301-K) [Fig. 2.3(b)].
The piezo rotates and translates the grating, scanning the laser frequency by mod-
ifying the cavity length and grating angle. The rotation point of the grating is chosen
carefully so the wavelengths selected by the cavity length and grating angle change
at the same rate during scanning, increasing the mode-hop free tuning range [59–61].
The grating angle is coarsely set by the placement of the grating mount with the aid
of an alignment rod, and finer adjustments are made with the set screw that resides
behind the piezo stack. We glued a bar magnet (K&J Magnetics) onto the top of
29
Fine- 
Adjustment 
Screw
Grating 
Mount Diode 
Mounting
Block
Grating
Piezo
Exit 
Window
Upper
Base 
Plate
Laser-Housing
Base Plate
Top View
Upper
Base Plate
Laser-Housing
Base Plate
Fine- 
Adjustment 
Screw
Lid
(c)
Damping 
Plate Sorbothane
Lower
Base Plate
Grating Mount Diode Mounting
Block
Thermo-
Electric 
Cooler
(b)
(a)
Side View
Figure 2.3. Schematic diagram and picture of the master laser. (a) Side view
showing the upper and lower base plates, fine-adjustment screw, grating mount,
diode mounting block, thermo-electric cooler, laser-housing base plate, sorbothane,
damping plate and polycarbonate lid. (b) Top view showing the grating mount,
grating, piezo, fine-adjustment screw, diode mounting block, laser-housing base plate,
and exit window. (c) Top-view picture of the master laser.
the grating lever arm to help damp its vibrational resonances, improving the laser’s
stability.
30
The upper base plate attaches to the lower base plate, and has two sections of
different thickness separated by a thin connection that allows for flexing [Fig. 2.3(a)].
The grating mount and the diode mounting block attach to the upper base plate on
opposite sides of the thin, flexing region. Another fine-adjustment screw (New Focus
P/N 9312-K) is placed between the upper and lower base plates, which allows for
vertical alignment of the grating by tilting the upper base plate. The laser housing is
the same as for the slave laser, except for the larger size and the addition of a damping
plate. The damping plate consists of a piece of aluminum attached to the bottom
of the laser-housing base plate with a piece of sorbothane sandwiched in between
[Fig. 2.3(a)]. This arrangement damps mechanical vibrations of the laser-housing
base plate that affect the laser’s stability.
2.3.3. Locking the Slave to the Master
The addition of the grating in the master laser reduces the output power to about
25 mW, which is not sufficient to create two MOTs after accounting for losses from the
myriad of optical components needed to stabilize and control the laser frequency, and
the ∼50% loss from transporting the light via optical fibers. To achieve the necessary
power, we feed a small amount of master-laser light into two slave lasers, which forces
the slave lasers to lase with the same spectral characteristics as the master laser.
This process is called “injection-locking,” and harnesses the power of the slave lasers
(about 50 mW) while retaining the narrow linewidth and frequency stability of the
master laser. Typically, we feed about 4 mW of master laser light through the second
31
rejection port of each slave laser’s optical isolator [62] and monitor the output of the
slave lasers on a 1.5 GHz, home-built Fabry-Perot cavity to verify locking. When
locked, we see only one peak in the Fabry-Perot spectrum—corresponding to the
master-laser frequency—while two peaks are visible if the slave laser is unlocked; one
at the master-laser frequency and one at the free-running slave-laser frequency.
As we mentioned in Section 2.3, two different laser frequencies are required to
create a MOT: the MOT cycling frequency, which excites the F = 2→ F ′ = 3 87Rb D2
hyperfine transition, and the repumping frequency, which excites the F = 1→ F ′ = 2
hyperfine transition (Fig. 2.4). The MOT cycling transition, often referred to as
the “MOT-trapping” transition, is responsible for cooling the atoms (Section 1.4).
The repump simply returns atoms that fall into the F = 1 ground state back into
the cycling transition so they can participate in the cooling process. Each of these
frequencies has a master laser dedicated to providing frequency-stabilized laser light
to the two MOTs. The frequency stabilization scheme involves active feedback control
of the laser frequency by “locking” it to a narrow spectroscopic feature, as well as
precise frequency shifts using acousto-optic modulators (AOMs). We will describe
both of these aspects in the next two sections.
2.3.4. Acousto-Optic Modulators
We will give a brief description of acousto-optic modulators (AOMs) first [53],
since they play an important role in many aspects of our experiment. An AOM
uses sound waves to create a moving, periodic variation in the index of refraction
32
Spherical
Square
Viewport
Differential-
Pumping Tube
Ion
Pump
Valve
Rb Source
Mounting
Post
(a) (b)
5  S2 1/2
5  P2 3/2
780 nm
(384 THz)
F=1
F=2
F!=0
F!=3
..
.
6.8 GHz
0.5 GHz
Rb87 D2 line
MOT
Repump
Figure 2.4. Hyperfine structure for the 87Rb D2 transition showing the relative
frequencies of the different levels and the MOT and repump transitions.
of a crystal, which shifts the frequency and direction of an incident laser beam by
diffraction from the index variation. The phonons are generated by driving a piezo
affixed to the crystal at radio frequencies (RF) up to several hundred MHz. A first-
order diffraction efficiency of about 80% can be achieved when the light is incident
on the crystal at the Bragg angle, θB = λ/2Λ (for small angles), where λ is the
laser wavelength and Λ is the sound wavelength. The diffracted beam forms an
angle θ = 2m θB with respect to the zero-order diffraction beam, where m is the
diffraction order, thus changing the direction of the beam. The AOM also shifts the
laser frequency up or down by integer amounts of the driving frequency, where the
integer equals the diffraction order. In addition to frequency shifting, we use the
AOM as a fast shutter (sub-µs shuttering time) and attenuator for light in the non-
33
zero diffraction orders by reducing the piezo’s driving voltage or switching it on and
off.
Driving and controlling the AOMs requires three different electronic components:
an RF signal generator, a digital RF switch for shuttering, and an RF amplifier
to create the power needed to drive the piezo. All three of these components were
designed and built in house by Peter Gaskell. The RF signal is generated by a voltage-
controlled oscillator with a 50− 100 MHz range, and the surrounding circuitry allows
for manual and computer control of the frequency and amplitude of this signal, as
well as an output for monitoring the frequency.
Since the AOM shifts the direction of the laser beam proportional to the driving
frequency, applications that involve changing the driving frequency require double-
passing the laser through the AOM. This technique ensures the beam remains aligned
with the optics placed downstream from the AOM despite the shifting direction. The
optical setup for double-passing an AOM is shown schematically in Figure 2.5. The
basic idea consists of focusing the beam at the center of the AOM, retro-reflecting the
first-order diffraction beam from a judiciously-placed spherical mirror back through
the AOM, and then using a polarizing beam splitter cube (PBSC) to separate the
frequency-shifted light. We place the spherical mirror a distance equal to its radius
of curvature from the beam’s focus in the center of the AOM, so that all the light
is reflected back through the focus regardless of any changes in beam direction. The
second pass through the AOM shifts the light’s frequency again, resulting in a total
34
Slave
Laser
Isolator
Vapor Cell
Anamorphic
Prism Pair
PBSC
f = 500 mm
3/8” Window
Lens
AOM
R = 500 mm
Spherical
Mirror
Lens
f = 50.2 mm
Differential
Photodetector
Mirror 1
Figure 2.5. The optical setup for double-passing an acousto-optic modulator
(AOM), including the polarizing beam splitter cube (PBSC), lens, AOM, quarter-
wave plate, and spherical mirror.
frequency shift of twice the driving frequency. It also changes the direction of the
beam a second time, such that it overlaps with the incoming, unshifted beam. To
separate the beams we horizontally polarize the incoming beam and pass it through
a PBSC before sending it through the AOM. A quarter-wave plate placed between
the AOM and the spherical mirror rotates the polarization the same direction on
each pass, resulting in vertically polarized light that the PBSC separates from the
incoming, horizontally polarized light. We use a 500 mm focal length lens and an
R = 500 mm spherical mirror with a 99% reflection coating at 780 nm from VLOC.
2.3.5. Frequency Locking
We create the MOT by exciting specific hyperfine energy levels that are separated
by only a couple hundred megahertz, which requires laser frequencies stable to about
1 part in 109. Despite the master laser’s current and temperature stabilization, the
frequency of the laser still drifts significantly over time, making active feedback control
of the frequency necessary. To accomplish this, we use a home-built PID feedback
control circuit designed by Daniel Steck. This circuit supplies multiple components
35
of the laser operation and frequency control electronics, including a lock-in amplifier,
a local oscillator for lock-in detection, a ramp generator and driver for the laser’s
piezo, and feedback control for the laser current and the piezo voltage. We use this
circuit to “lock” the laser frequency to a specific hyperfine transition obtained through
saturated-absorption spectroscopy [37, 54, 63, 64].
At room temperature, the atomic velocities in a rubidium vapor cell are large
enough that the Doppler-broadened linewidth (∼500 MHz) washes out all the hyper-
fine structure when using regular absorption spectroscopy. Saturated-absorption
spectro-scopy involves a pump-probe setup that eliminates the problem of Doppler-
broadened absorp-tion spectra, providing resolution high enough to distinguish the
hyperfine structure of 87Rb. The basic setup involves overlapping a strong pump
beam with a weak, counter-propagating probe beam derived from the same laser, and
monitoring the transmission of the probe beam. As the laser frequency is scanned,
the pump and the probe come into resonance with different groups of atoms that have
opposite velocities, as the positive-velocity group shifts into resonance with one beam,
and the negative-velocity group shifts into resonance with the counter-propagating
beam. This results in almost entire absorption of the weak probe beam, creating
a Doppler-broadened absorption profile. This situation changes, however, for atoms
with near-zero velocity, since the pump and probe frequencies are not Doppler shifted.
When the laser frequency scans over a hyperfine resonance, the v = 0 atoms are
resonant with both beams simultaneously, and as a result become saturated by the
36
strong pump, which increases transmission of the probe. This produces a Doppler-
broadened transmission spectrum at most frequencies, with small peaks due to the
increased transmission at the frequency of each hyperfine resonance [Fig. 2.6(a)].
These peaks are called “Lamb dips” (they appear as dips if the transmission spectrum
is inverted to show absorption) [37], and their width is on the order of the natural
linewidth (∼38 MHz). Additional peaks are also observed in this spectrum, which
occur at frequencies where atoms with a particular velocity have one hyperfine tran-
sition down-shifted into resonance with one beam, and another hyperfine transition
up-shifted into resonance with the other beam. This type of resonance is referred to
as a “crossover transition,” and the increased transmission is due to depletion [37]
rather than saturation. Depletion has a greater effect on the transmission, leading to
the more prominent spectral features observed for the cross-over transitions.
2.3.6. Saturated-Absorption Spectroscopy Setup
The basic saturated-absorption spectroscopy optical setup is shown in Figure 2.7,
which we use for the repumping master laser. This scheme sends a small amount of
master-laser light through a 3/8′′ thick window (CVI Laser P/N PW-1037-C), which
produces two parallel, weak reflections (one from each surface), while the majority
of the light transmits through. The two reflected beams (probe beams) pass through
a rubidium vapor cell, while the transmitted beam (pump beam) reflects from three
mirrors and passes through the cell in the opposite direction, nearly overlapping one
of the probe beams. We call the overlapped beam the “probe beam” and we refer to
37
probe wavelength probe wavelengthd
if
fe
re
n
ti
a
l 
p
h
o
to
d
e
te
c
to
r
s
ig
n
a
l
p
ro
b
e
 t
ra
n
s
m
is
s
io
n (a) (b)
F!=3
F!=1
F!=2,3
F!=1,3
F!=2
F!=3
F!=1
F!=2,3
F!=1,3
F!=2
F=2       F!
F!=1,2
F!=1,2
Rb,87 F=2       F!Rb,87
Figure 2.6. The saturated-absorption spectrum for the 87Rb F = 2 → F ′
hyperfine transition. (a) Transmission of the probe beam as a function of the laser
wavelength showing the saturated-absorption peaks. (b) Signal from the differential
photodetector, which subtracts out the Doppler-broadened background, making the
saturated-absorption peaks more visible. These spectra were provided by D. A. Steck.
the other beam as the “reference beam.” We focus the probe beam and the reference
beam onto a home-built, differential photodetector, comprised of two photodiodes
and a circuit that subtracts the two signals. The reference beam simply exhibits the
Doppler-broadened transmission profile, while the probe-beam spectrum also contains
the saturated-absorption peaks [Fig. 2.6(a)]. The differential photodetector subtracts
the Doppler-broadened background from the probe-beam spectrum, allowing us to
view the saturated-absorption peaks more clearly [Fig. 2.6(b)].
We lock the repump laser to the F = 1 → F ′ = 1, 2 crossover transition because
it is the largest peak in the F = 1 → F ′ spectrum. The frequency of this transition
is 78.5 MHz lower than the F = 1→ F ′ = 2 repump transition (Fig. 2.4), so we use
an 80 MHz AOM (IntraAction P/N ATM-801A2) to shift the frequency to resonance
and to attenuate and shutter the beam as well.
38
Slave
Laser
Isolator
Vapor Cell
Anamorphic
Prism Pair
PBSC
f = 500 mm
3/8” Window
Lens
AOM
R = 500 mm
Spherical
Mirror
Lens
f = 50.2 mm
Differential
Photodetector
Mirror 1
Figure 2.7. Schematic of the of the optical layout for saturated-absorption
spectroscopy. A thick window splits the beam into a strong pump beam and two
weak probe beams, which pass through a rubidium vapor cell and a lens into a
photodetector that subtracts their signals. The pump beam wraps around and
propagates through the vapor cell in the opposite direction, overlapping one of the
probe beams.
To perform lock-in detection on the saturated-absorption signal, we modulate the
laser injection current at 200 kHz, which in turn modulates the frequency of the laser.
The photodiode signal, which registers the frequency modulation as shifts in intensity
from moving on and off of resonance, is then fed into the lock-in amplifier to create an
error signal for feedback control of the piezo and the current. The original saturated-
absorption signal [Fig. 2.6(b)] is not a good candidate for feedback control because
the desired frequency is at a maximum in intensity, so small frequency drifts produce
undetectable changes in the magnitude of the signal. The error signal, however,
generated from the frequency modulation and phase-sensitive lock in detection, has
a dispersive line shape with a large slope at the frequency of interest [65], such that
small changes in frequency create large, detectable changes in the magnitude of the
signal.
39
An additional feature of the lock-in circuit is the ability to feed a small amount
of the piezo output to the laser injection current. Though this does not improve
its lock-in stability, it increases the mode-hop-free tuning range of the laser when
scanning the piezo by changing the injection current to better match the frequency
to the longitudinal mode of the cavity as it changes length.
The optical setup for locking the MOT master laser is slightly more complicated
to avoid modulating the laser frequency directly, as in the case of the repump. MOTs
are not very sensitive to the frequency of the repump light, so the small frequency
modulation does not concern us. MOTs are, however, very sensitive to the detuning
of the cycling transition, so a small amount of frequency modulation is not desirable.
We modulate the saturated-absorption signal for the MOT laser by double-passing
the pump beam through a 145 MHz AOM (IntraAction P/N ATM-1451A2), whose
driving frequency is modulated from 143 to 147 MHz at a frequency of 200 kHz.
The optical setup is the same as for the repump laser (Fig. 2.7), except we replace
mirror 1 with the double-passing optics shown in Fig 2.5. Though we do not modulate
the frequency of the detected reference beam directly, the frequency where the Lamb
dips occur depends on the difference between the pump and probe frequencies, so the
modulation moves the peak of the Lamb dip relative to the fixed probe frequency,
modulating the intensity reaching the photodiode.
As with the repump, we lock the MOT laser to the largest feature in the saturated-
absorption spectrum, the F = 2 → F ′ = 2, 3 crossover transition. Due to the
40
frequency shift from the AOM in the saturated-absorption spectroscopy setup, the
crossover transition occurs 278.3 MHz below the F = 2 → F ′ = 3 cycling transition
(Fig. 2.4). We shift the laser frequency to resonance using three 80 MHz AOMs;
one that is double-passed and used to control the detuning (IntraAction P/N ATD-
801A2), and one that also serves as an attenuator and shutter on the output of each
slave laser (IntraAction P/N ATM-801A2). We send the zero-order diffraction beam
from the AOMs on the output of each slave laser to a Fabry-Perot cavity (switching
between them with a flip mirror) to verify each slave is locked to the master laser. This
optical setup is illustrated schematically in Figure 2.8. We can change the frequency
of the AOM that controls the detuning from 60 to 100 MHz, allowing us to detune
the laser from 78.3 MHz below the cycling resonance to 1.7 MHz above it.
2.3.7. Fibers and Fiber Coupling
We divided our optical table into an optics side, containing the optical setup
described above, and a vacuum-chamber side, where we perform the experiments.
To transport the laser light to the experiment, we use single-mode, polarization-
maintaining, FC/APC connected fibers (Oz Optics P/N PMJ3A3A-850-5/125-3-*-
1) of various lengths (indicated by the *). We use Thorlabs collimators (Thorlabs
P/N F220FC-B) that produce a nearly collimated, 2.1 mm diameter beam (1/e2
intensity diameter) for most applications. Coupling a laser into a single-mode fiber
can be a tedious process, and we typically use a setup that involves a one-to-one
telescope to ensure collimation of the beam and a fixture to hold the collimator. The
41
Slave
Laser
Slave
Laser
MOT
Master Laser
Repump
Master Laser
Saturated-Absorption
Spectroscopy
Saturated-Absorption
Spectroscopy
AOM
AOM
AOM
AOM To Pyramid
MOT
To Pyramid
MOT
To Second
MOT
To Second
MOT
double-passed
Fabry-
Perot
Cavity
Flip Mirror
Figure 2.8. Schematic of the basic optical setup for producing the MOT-trapping
and repump light, showing the relative layout of the master lasers, slave lasers,
saturated-absorption spectroscopy optics, frequency-shifting AOMs, and Fabry-Perot
cavity.
fixture attaches to a mirror mount and has two fine-adjustment screws that provide
horizontal and vertical translation of the collimator (Fig. 2.9). The mirror mount
allows for tilting, and the combination, along with appropriate placement of the
second telescope lens, produces about 50% coupling efficiency for the non-Gaussian
output of a diode laser.
For the pyramid MOT, we couple both the repump and MOT light into one fiber
using a PBSC. We couple the repump light directly into the fiber collimator using
the fixture, while we steer the MOT beam in using two mirrors. The fiber output has
no collimating lens, so the light is essentially emitted from a point source, which we
42
Figure 2.9. Picture of the fixture for coupling the fiber attached to a mirror mount,
showing the fiber, collimator, and horizontal- and vertical-adjustment screws. The
mirror-mount-adjustment screws are barely visible.
pass through a quarter-wave plate and collimate into a large diameter beam using a
200 mm focal-length, 3′′ diameter lens (Thorlabs P/N LA1353-B).
The second MOT requires the six traditional laser beams, so we purchased a six-
way, fiber-optic beamsplitter array (Canadian Instrumentation and Research, custom
design) with two inputs (one for the repump light and one for the MOT light) and
six outputs. The power from each input is distributed fairly evenly (±3% of the total
output) amongst the six individual outputs, though we matched outputs with similar
powers to form the three opposed beam-pairs. Temperature fluctuations of the box
where the beam splitting occurs shifts the interference pattern of the overlapped,
opposing beams enough to significantly distort the MOT, so we actively temperature
stabilize this part of the device using a thermo-electric cooler and a laser-temperature-
control board. Each output fiber connects to a large output collimator (Thorlabs P/N
F810FC-780) that produces a 6.6 mm diameter beam (1/e2 intensity diameter). We
43
secure each collimator in a mirror mount to provide steering capability, and affix
a quarter-wave plate (Casix P/N WPL1225-lambda/4-780nm-M) in front of each
output lens to produce the circularly-polarized light required for the MOT.
2.3.8. Optical Setup
Combined together, the different optical pieces of our experiment are impressive,
covering about 25 square feet of our optics table with over 175 individual elements.
A picture of the optical table is shown in Figure 2.10. Tao Li’s dissertation [58] has
a comprehensive schematic showing the placement of most elements.
2.4. Vacuum Chamber
To cool, trap and control atoms effectively, we carry out our experiments in ultra-
high vacuum (UHV), which typically refers to pressures below ∼ 10−8 torr. Low
background pressure significantly increases lifetimes of the trapped atoms by reducing
the number of collisions with background gases. Our UHV system consists of a
chamber divided into a high-pressure side (∼10−8 torr) and a low-pressure side (.
10−10 torr), separated by a differential-pumping tube [58]. Here, “high-pressure”
simply indicates that the pressure is high relative to the low-pressure side. The
differential-pumping tube consists of a cylinder, several inches long, with a tapered
hole bored through the center [Fig. 2.11(a)]. Connecting the tapered end to the high-
pressure side of the chamber impedes the flow of gas particles to the low-pressure
side, helping to maintain a pressure differential between the two sides. The divided
44
Figure 2.10. Picture of the optical table showing the lasers and multitude of optics
needed to produce the MOT trapping and repump light. Two slave lasers are visible
on the near side of the table and four master lasers are visible on the far side.
Several racks of electronics that control and monitor the experiment can be seen
in the background.
chamber allows us to trap large numbers of atoms at very low pressures, creating a
versatile setup for a wide range of atom-optics experiments.
2.4.1. High-Pressure Side
The high-pressure side of the chamber includes the rubidium source, the mirrors
for the pyramid MOT, an ion pump, a pair of anti-Helmholtz coils, and three pairs
of Helmholtz coils. The main body of the chamber consists of a Kimball Physics
“spherical square” (P/N MCF450-SS20400-A), which has two, 4.5′′ conflat (CF) ports
45
Spherical
Square
ViewportPyramid-MOT
Mirrors
Differential-
Pumping Tube
(a) (b)
Bellows
Ampoule 
Breaker
Viewport Valve
Connection
Ampoule
Figure 2.11. The high-pressure side of the chamber. (a) Schematic diagram of the
differential-pumping tube, spherical square, pyramid-MOT mirrors, and viewport.
(b) Picture of the pyramid-MOT mirrors mounted on the end of the differential-
pumping tube, showing the small hole in the center.
opposite each other, plus four additional 2.75′′ CF ports spaced 90◦ apart. One 4.5′′
CF port connects to our custom-designed differential-pumping tube, which includes
a structure for mounting the pyramid-MOT mirrors [Fig. 2.11(a)] that extends into
the spherical square. The MOT light enters the chamber through a 4.5′′ CF, zero-
length, AR-coated, quartz window (Larson Electronic Glass P/N VQZ-250-F4, AR
coated by Spectrum Thin Films) that we connected to the other 4.5′′ CF port opposite
the pyramid-MOT mirrors. The pyramid-MOT mirrors are tear-drop shaped Pyrex
pieces with a notch at the vertex, cut with a water jet at a local company. The pyrex
was reflection coated (by Spectrum Thin Films) with the constraint of minimizing
the phase-shift differences of the MOT-light polarization upon reflection. We used
Vacseal (SPI Supplies P/N 05100C-AB), a UHV cement, to affix the mirrors into place
at the end of the differential-pumping tube prior to assembling the chamber. When
46
assembled, the mirrors form a pyramid with a small hole in the top [Fig. 2.11(b)]. A
circularly-polarized, large-diameter beam incident on the pyramidal mirror structure
will reflect in such a manner as to create the six counter-propagating beams (with the
correct polarization) necessary to form a MOT inside the pyramid. Atoms trapped in
the center of the structure do not experience a counter-propagating laser beam due
to the small hole at the apex and get pushed through the hole and the differential-
pumping tube into the low-pressure side of the chamber [66–68].
A crushed rubidium breakseal ampoule (Alfa 10315 1g) contained in a 1.33′′ CF
tee creates our source of rubidium vapor. We crushed the ampoule under vacuum
using a steel rod welded to a 1.33′′ CF blank that we attached to a 3′′ long, 1.33′′
CF, bellows (MDC P/N 400000) (Fig. 2.12). When the bellows are compressed,
the rod makes contact with the ampoule, allowing us to crush it. We verified a
successful crush by looking through a small viewport (Larson Electronic Glass P/N
VPN-075-F1) attached to one end of the tee. Four small Kapton heaters (Minco P/N
HK5161R78.4L12A) wrapped around the tee allow us to heat the rubidium source to
increase the background pressure in the chamber and also to prevent rubidium from
condensing on the viewport. We connected a valve (Varian P/N 951-5027) between
the source and a 2.75′′ CF port on the spherical square to control the amount of
rubidium in the chamber.
We connected a 20 L/s ion pump (Varian Model VacIon Plus Starcell 20) to the
top 2.75′′ CF port of the spherical square to help maintain the vacuum, though we
47
Spherical
Square
ViewportPyramid-Mot
Mirrors
Differential-
Pumping Tube
(a) (b)
Bellows
Ampoule 
Breaker
Viewport Valve
Connection
Ampoule
Figure 2.12. Schematic diagram of the rubidium source, showing the ampoule,
viewport, valve connection, bellows and ampoule breaker.
do not use it anymore because the rubidium poisoned it early on. This does not
pose a problem since we carefully control the flow of rubidium using the valve on
the source, and other pumps in the system also help keep the pressure down. We
attached a second valve (Varian P/N 951-5027) to the third 2.75′′ CF port on the
spherical square, allowing us to connect a turbo pump to the chamber for the initial
pump down. The last port, located on the bottom of the spherical square, connects
to a 2.75′′ CF blank attached to a post for mounting on the optical table. Figure 2.13
shows the layout of the high-pressure side of the chamber.
Each anti-Helmholtz coil consists of 23 AWG, round magnet wire (purchased from
MWS) wrapped 400 times around a 4.75′′ diameter groove in an aluminum ring,
held in place with high-temperature epoxy (Epoxy Technology P/N 343ND). The
coils are spaced 4.2′′ apart and generate an ∼11 G/cm magnetic-field gradient in
the trapping region with about 1.3 A of current. A temperature sensor (Analog
Devices P/N AD590JH) is inserted into each aluminum ring, allowing us to monitor
the temperature to ensure the coils do not overheat. We constructed three pairs
48
Spherical
Square
Viewport
Differential-
Pumping Tube
Ion
Pump
Valve
Rb Source
Mounting
Post
(a) (b)
Figure 2.13. The different components connected to the spherical square. (a)
Schematic diagram of the high-pressure side of the chamber, including the spherical
square, differential-pumping tube, viewport, ion pump, rubidium source, valve to
connect the turbo pump, and mounting post. (b) Picture of the high-pressure side of
the chamber with all components visible except the differential pumping tube.
of Helmholtz coils (one for each dimension) by wrapping 10-conductor ribbon wire
(Mouser P/N 517-3801/10) around rectangular frames. We built the frames by joining
various lengths of 5/8′′× 1/4′′ plexiglass to aluminum L-brackets with 24 hour epoxy
(GC Electronics P/N 10-347). We used double-sided tape to temporarily hold the
layers together during winding, then added small cable ties to permanently secure the
layers to the frames. The ends of the ribbon cable were outfitted with a double-row
socket (Mouser P/N 517-89110-0101), allowing us to connect the 10 conductors into
one long wire using a header (Digikey P/N 929665-09-36-N). We designed the coils
to produce at least a 1 G/A magnetic field at the center of each pair (2 G/A along
the anti-Helmholtz-coils’ axial direction), with the constraint of fitting around the
49
spherical square and its surrounding equipment (including the anti-Helmoltz coils).
The resulting coil-pair specifications are detailed in Figure 2.14.
The current supplied to the Helmholtz and anti-Helmholtz coils comes from home-
built current drivers backed by a 40 V, 10 A power supply (that we usually run at
30 V). The current drivers provide several amps of bi-directional drive capability,
manual current control, a current-modulation input, digital on/off switching, and a
small LCD screen that conveniently displays the amperage. Each pair of Helmholtz
coils has its own dedicated driver, while the anti-Helmholtz coils have one driver for
each coil (the current has to go in opposite directions). The two anti-Helmoltz-coil
drivers are actually slightly different circuits, connected in a master-slave config-
uration. In this configuration, the master board controls the current output of the
slave board, which is proportional to the master current, and the proportionality
factor can be changed manually. Though it has not really been a problem, each board
has an automatic shutdown should the temperature of the coils or the high-current
op amps get too high. There are three red LEDs that indicate the different modes
of shutdown: user shutdown, coil overheating, and chip overheating. Additionally,
an LCD screen displays the temperature of each coil if an IC temperature sensor
(AD590) is affixed to the coil. Typically, we operate the anti-Helmholtz coils at
−1.21 A and −0.98 A for the master and slave, respectively, while the x, y, and z
Helmholtz coils are set to 0.45 A, −0.70 A, and 0.00 A respectively, which places the
50
x
Anti-
Helmholtz
Coils
z
y
Coil
Dimensions
(inches)
Separation
(inches)
Turns
Gauss/Amp 
at Center
x 12 x 9 6.5 3 1.7
y 12.4 x 10.8 6.2 3 1.7
z 13.4 x 13.4 8 6 2.6
Figure 2.14. The x, y, and z Helmholtz-coil-pair specifications for the pyramid
MOT, including a diagram indicating the orientation of the three dimensions relative
to the anti-Helmholtz coils and the low-pressure vacuum-chamber assembly.
MOT in front of the hole in the pyramid-MOT mirrors. We note that these values
may need adjustment over time to maintain the position of the MOT.
2.4.2. Low-Pressure Side
The low-pressure side of the chamber includes several vacuum pumps, mirrors for
dumping the dipole-trap beam, a pair of anti-Helmholtz coils, three pairs of Helmholtz
coils, and an 8′′ long, fused-silica (Spectrosil 2000) vacuum cell where we conduct the
experiments. The main body consists of a Kimball Physics “spherical cube” (P/N
MCF450-SC60000-C), which is essentially a cube with rounded corners and a 4.5′′ CF
port on each face. Inside the cube we mounted two mirrors (Thorlabs P/N BB3-E03)
(Fig. 2.15) to reflect the dipole-laser light out of the chamber and into a beam dump.
We accomplished this by bolting a custom-built base plate and two mirror mounts to
a pair of Kimball Physics groove grabbers (P/N MCF450-GG-CT02-A), specifically
designed for mounting items in their chambers (Fig. 2.15). The two (opposite facing)
ports dedicated to dumping the dipole-trap beam are sealed with 4.5′′ CF, zero-length,
51
Groove
Grabbers
Viewport
Spherical
Cube
Dipole-Trap
Beam
Base
Plate
Mirrors
Grooves
Figure 2.15. Schematic diagram of the low-pressure side of the chamber viewed from
the top, showing the spherical cube, viewports, grooves, groove grabbers, mirrors, and
the base plate for mounting the mirrors.
AR-coated, glass viewports (Larson Electronic Glass P/N VP-250-F4, AR coated by
Spectrum Thin Films).
The top port connects to a 4.5′′ CF cross, where we connected a 75 L/s ion pump
(Varian VacIon Plus Starcell 75), a Ti-sublimation pump (Duniway Stockroom P/N
TSP-275-003) and a valve (Varian P/N 951-5027) to connect to the turbo pump for
the initial pump down (Fig. 2.16). The ion pump runs continuously after the chamber
is pumped down, and is primarily responsible for keeping the background pressure
low. The Ti-sublimation pump works by coating the chamber walls surrounding
the titanium filament with clean titanium, which then reacts with any colliding
background gases, reducing the pressure. We attached the Ti-sublimation pump to
the cross via a large elbow (Fig. 2.16) to prevent the filament from spewing titanium
52
Figure 2.16. Picture of the CF cross mounted on the spherical cube, showing the
attached ion pump (right), valve (top), elbow and Ti-sublimation pump (left).
into delicate parts of the chamber, and we only run it occasionally to reduce small
increases in pressure. We do this by running 50 A of current through the filament
several times for 2 minutes each time (a process referred to as “flashing”), which
temporarily increases the background pressure for a few minutes until the released
titanium begins pumping.
The bottom port connects to a 4.5′′ CF blank that we modified by inserting five
electrical feed-throughs where we mounted five getters (SAES P/N ST175/HI/16-
30/300C). Getters provide additional vacuum pumping capability, especially for hy-
drogen, which dissolves and diffuses into the bulk getter material. To maintain the
pressure in the chamber, we occasionally run current through the getters (8.5 A,
for 2 minutes, several times), which improves their pumping efficiency after a brief,
initial increase in pressure. We typically do this in conjunction with flashing the Ti-
53
sublimation pump, which pumps the hydrogen released by the getters. We alternate
between the Ti-sublimation pump and the getters, waiting for the initial pressure
increase to subside between each start. We bolted the modified blank to a steel base
plate with a circular cut-through such that the getter connections are accessible, then
secured the steel plate to the optical table to mount the chamber (Fig. 2.17).
The large-bore side of the differential-pumping tube attaches to one of the two
remaining 4.5′′ CF ports in the spherical cube. The end of the tube extends out into
the chamber, over the location of the dumping mirrors (Fig. 2.17), which we placed
lower than the end of the tube so as not to interfere with the exiting atomic beam
from the pyramid MOT. We mounted a custom-built, square vacuum cell (by Hellma)
(Fig. 2.17) onto the remaining port, opposite the differential-pumping tube. Atoms
launched from the pyramid MOT through the differential-pumping tube pass into the
vacuum cell, where they are captured by the second, six-beam MOT [69]. For this
MOT, four of the beams are aligned parallel to the table and enter the cell at 45◦
angles, while the other two beams are mounted vertically above and below the cell.
This design rapidly transports large numbers of atoms into the low-pressure vacuum
cell while maintaining the pressure differential between the two chambers.
Initially, we valiantly attempted to construct our own vacuum cell, using pieces of
Pyrex cut with a water jet and Vacseal. We started by verifying we could achieve UHV
pressures with a fused-silica window Vacsealed onto a conflat flange. We refined our
technique over many iterations, reaching pressures in the 10−8 torr range that survived
54
Spherical
Cube
Hellma
Cell
Base
Plate
Groove
Grabber
Getters
Mirror
Differential-
Pumping Tube
Blank with
Feed-Throughs
Hellma
Cell
Fused-Silica
Flange
4.5” CF
Flange
2.75” CF
Flange
Metal
Gasket
Vacuum
Screws
Figure 2.17. Schematic diagram of the low-pressure side of the chamber viewed
from the side, including the spherical cube, differential-pumping tube, Hellma cell,
dumping mirror, groove grabber, getters, the blank containing the electrical feed-
throughs for the getters, and the mounting base plate.
bake outs to 200◦C and passed helium leak tests on several occasions. Creating a UHV
seal with Vacseal required a meticulous, multi-step process, with four key components:
an even application of Vacseal to both contact surfaces, a quick (30 minute) bake
at 170◦C to evaporate some of the solvents, contacting the surfaces while still hot,
and baking overnight at 250◦C while keeping reasonable pressure on the contacted
surfaces. After experimenting with the fused-silica window, we put our efforts towards
building a Pyrex vacuum cell. The multiple pieces needed to construct the vacuum
cell significantly complicated the aforementioned sealing process. We started using
teflon tape [Fig. 2.18(a)] to guide the application of the Vacseal and restrict it from
flowing during a brief (10 minute) bake at 170◦C. This brief bake was introduced to
55
(a) (b)
I
z
z
y
F
za
a
< 0! 
(a)
(b)
(c)
Figure 2.18. Pictures showing the assembly of our home-built vacuum cell. (a) We
used teflon tape to prevent the Vacseal from flowing during a 10 minute bake. (b) The
jig we designed to hold the four sides of the cell together during the baking process.
prevent the Vacseal from dripping while we mounted the pyrex pieces in a jig that
held them in place during the 30 minute bake [Fig. 2.18(b)]. This jig held the pieces
together during the longer bake as well. We also had to assemble the vacuum cell
in two parts, first constructing the main body (including the overnight bake), then
attaching the end piece to the body and the body to the circular flange with a second
overnight bake. Polishing the cut edges of the pyrex pieces that contacted the flat
surfaces proved advantageous as well. While we met with some success after four
attempts, reaching a pressure of ∼1 × 10−7 torr before baking our home-built cell
(after the bake we lost a couple orders of magnitude), we were unable to reliably
produce a robust, leak-free seal along all the joints. We eventually abandoned this
effort and purchased a custom cell from Hellma.
A second challenge came from devising a reliable, leak-free method for connecting
the Hellma cell to the vacuum chamber since the Vacseal approach did not pan out.
56
Spherical
Cube
Hellma
Cell
Base
Plate
Groove
Grabber
Getters
Mirror
Differential-
Pumping Tube
Blank with
Feed-Throughs
Hellma
Cell
Fused-Silica
Flange
4.5” CF
Zero-Length
Reducer
2.75” CF
Flange
Metal
Gasket
Vacuum
Screws
Figure 2.19. Schematic diagram showing the cross-section of the Hellma cell
mounting apparatus, including the 4.5′′ zero-length reducer, the 2.75′′ flange, lead-
alloy gaskets, vacuum screws, Hellma cell, and fused-silica flange.
To this end, we modified a 4.5′′ to 2.75′′ CF, zero-length reducer and a 2.75′′ CF
flange to have recesses that fit the circular, fused-silica flange (Fig. 2.19). We then
slipped the modified, 2.75′′ CF flange over the Hellma cell, sandwiching the fused-
silica flange between the two steel CF flanges, with thin lead-alloy gaskets (Indium
Corp Indalloy 165) placed between the metal and fused silica surfaces [70]. The
gaskets are compressed with standard, silver-plated vacuum screws equipped with
pairs of opposed Belleville disc springs (MSC 87779211). The gasket underneath the
flange forms the vacuum seal by flattening onto the fused-silica and steel surfaces
during compression, while the second gasket simply serves as padding to prevent the
steel from cracking the fused-silica flange. Initially we tried using gold gaskets, which
performed well on circular, fused-silica blanks, however, we cracked a Hellma cell
trying to compress the gold gaskets to eliminate a leak. This led to our use of the
softer lead-alloy gaskets. A picture of the mounted Hellma cell is shown in Figure 2.20.
57
Spherical
Square
Viewport
Differential-
Pumping Tube
Ion
Pump
Valve
Rb Source
Mounting
Post
(a) (b)
5  S2 1/2
5  P2 3/2
780 nm
(384 THz)
F=1
F=2
F!=0
F!=3
..
.
6.8 GHz
0.5 GHz
Rb87 D2 line
MOT
Repump
Figure 2.20. Picture of the Hellma cell mounted using the modified 2.75′′ and 4.5′′
CF flanges with the lead-alloy gaskets.
To assess the performance of the gold and lead-alloy gaskets, we leak-tested the
various seals by attaching the component to our turbo-pump station and flooding the
sealed area with helium. During the flooding we monitored the helium pressure on the
turbo-pump station’s residual gas analyzer to detect any leaks. We performed the leak
tests before and after a brief bake at 200◦C, and we applied additional compression
as needed to fix any leaks that appeared.
The anti-Helmholtz coils for the second MOT are similar to those for the pyramid
MOT, consisting of the same wire wrapped 216 times around a circular, Delrin frame
with a 40 mm diameter. The coils attach to the 2.75′′ CF flange securing the Hellma
58
cell, and are separated by 50 mm, such that the Hellma cell just fits in between
them (Fig. 2.21). These coils generate about a 12 G/cm magnetic-field gradient
in the trapping region at 0.5 A of current. We constructed the Helmholtz coils in
a fashion similar to the pyramid-MOT Helmholtz coils described above, wrapping
ribbon wire around an aluminum frame that we bolted to the optical table. We chose
the specifications to accommodate the existing equipment, produce a field of about
1 G/A at the center of each coil pair (larger along the anti-Helmholtz-coils’ axial
direction), and ensure the frame formed a three-dimensional, rectangular box. The
specifications for the three pairs of Helmholtz coils are given in Figure 2.21.
The coil drivers for the second set of Helmholtz and anti-Helmholtz coils are
the same as described earlier, except we do not monitor the temperature of the
anti-Helmholtz coils. To form a fast-loading, strong MOT in the Hellma cell, we
typically operated the anti-Helmholtz coils at 0.68 A for the master and slave, and
the x, y and z Helmholtz coils at 0.02 A, −0.44 A, and −0.42 A, respectively. The
Helmholtz-coil values were chosen to prevent stray magnetic fields (i.e. earth’s) from
launching the atoms during fluorescence imaging (see Section 2.6). Our experiments
relied heavily on controlling the location of the MOT, so we altered these values
significantly depending on the needs of each experiment.
2.4.3. Vacuum Chamber Assembly
Achieving very low pressures in a vacuum chamber is as much superstition as it
is science; every group has slightly different procedures for cleaning and prepping the
59
probe wavelength probe wavelengthd
if
fe
re
n
ti
a
l 
p
h
o
to
d
e
te
c
to
r
s
ig
n
a
l
p
ro
b
e
 t
ra
n
s
m
is
s
io
n (a) (b)
F!=3
F!=1
F!=2,3
F!=1,3
F!=2
F!=3
F!=1
F!=2,3
F!=1,3
F!=2
F=2       F!
F!=1,2
F!=1,2
Rb,87 F=2       F!Rb,87
Helmholtz
Coils
Anti-Helmholtz
Coils
Coil
Dimensions
(inches)
Separation
(inches)
Turns
Gauss/Amp 
at Center
x 10 x 4.5 6 6 1.1
y 5.5 x 7 10 10 0.5
z 6 x 10 4.5 4 1.4
x
z
y
Hellma
Cell
Figure 2.21. The x, y, and z Helmholtz-coil-pair specifications for the second MOT,
including a diagram showing the arrangement of the Helmholtz and anti-Helmholtz
coils around the Hellma cell, as well as the orientation of the three dimensions relative
to the Hellma cell and optics table.
vacuum components that they swear by are critical to reaching optimum performace.
The main tenets are generally the same [71–73], and here we will document our
preferred practices.
Prior to assembling the different vacuum pieces (tees, crosses, valves, etc.), we
adhered to a strict baking and cleaning procedure. We start by baking the components
at 480◦C for 48 hours, which removes some dissolved hydrogen in the stainless steel
and forms an oxide layer on the surface that prevents hydrogen from diffusing through
[74, 75]. Parts that were machined or modified in-house had to undergo extensive
cleaning prior to baking, involving sonication in alconox and de-ionized water, then
rinsing with acetone and methanol. Though all the pieces are machined from 304
or 316 stainless steel, the finishes on the outer surfaces vary by finishing method,
producing remarkably different colors and hues after baking. Some of the more
exoticly-hued pieces are shown in Figure 2.22. After baking, we clean each piece
with spectroscopic grade acetone and then spectroscopic grade methanol, drying each
60
(a)
(c)
(b)
Figure 2.22. Pictures of three of the more stunning vacuum components after baking
for 48 hours at 480◦C. (a) the spherical cube, (b) the differential-pumping tube, and
(c) an AR-coated viewport.
component after each rinse with cool nitrogen gas (from an LN2 dewar). The cleaning
removes any contamination that may have occurred during the baking process. Once
clean, we wrap each component in oil-free, UHV aluminum foil (All Foils UHV
aluminum foil) to await assembly.
We assembled the chamber in pieces, taking care to cover any exposed CF ports
with UHV aluminum foil and clean each copper gasket with spectroscopic grade
acetone and methanol to prevent contamination. Certain components required as-
sembly in a specific order, such as placing one of the pyramid-MOT anti-Helmholtz
coils around the differential-pumping tube prior to attaching the spherical cube. Addi-
tionally, we installed the other set of anti-Helmholtz coils and both sets of Helmholtz
coils after baking the chamber out as they were not designed for high temperatures.
61
2.4.4. Baking Out the Vacuum Chamber
A common practice involves baking a vacuum chamber (typically at temperatures
near or above 200◦C) while pumping on it to remove excess water vapor and other
residual gases. This is usually the last step in the meticulous process to achieve UHV
pressures. As with cleaning the vacuum components, a plethora of bake-out methods
exist, each one unique to the lab and the chamber. We baked out our chamber four
times (for reasons we will explain below), and here we will describe the process.
In order to bake out our chamber, we built an oven around it made of UHV
aluminum-foil-covered fire bricks (Thermal Ceramics) (Fig. 2.23). This provided
sufficient insulation such that we could heat the inside to at least 200◦C without
posing a risk to the lab. We wrapped many meters of heater tape (Omega) around
the chamber and placed more on the floor of the oven, then inserted 16 thermo-couples
(wire from Omega, P/N GG-J-20-25) at various locations to monitor the temperature
in different regions. We powered the heater tape with variable transformers (Circuit
Specialists P/N TDGC2-2) and displayed the temperature data online with the help
of two home-built, ethernet enabled thermocouple monitors that interfaced with the
thermo-couples.
We initially pumped down and baked out our chamber without the Hellma cell
to test all the vacuum seals and our various pumps, and to see what pressure we
could achieve. To start this process, we attached our turbo-pump station to the
valves on the spherical cube and the spherical square to pump on both the high-
62
Figure 2.23. Picture of the partially-constructed oven made of vacuum-foil-covered
fire bricks we used to bake out the vacuum chamber. The cross and elbow wrapped in
heater tape, the top of the spherical cube and a few of the red variacs used to control
the temperature are visible in this picture.
and low-pressure sides of the chamber. The turbo-pump station consists of a turbo
pump (BOC Edwards P/N EXT 70H 24V) backed by a roughing pump, a residual
gas analyzer (Stanford Research Systems RGA 300) and various pneumatic valves.
This system can pump down to pressures on the order of 10−8 torr.
We started slowly heating up the oven after reducing the pressure to about 2 ×
10−8 torr with the turbo pump, taking care not to raise the temperature too quickly
or unevenly. This avoided rapid thermal expansion that could have compromised the
vacuum seals or the integrity of various components. We raised the temperature to
215◦C over the course of two and a half days, even though the viewports had 200◦C
temperature rating and the cable for the Ti-sublimation pump was non-bakable. We
63
held the temperature for seven days, turning the ion pumps on after two days, and
occasionally fiashing the Ti-sublimation pump and the getters. We cooled down over
one day, and noticed the Ti-sublimation pump was not working well. It turns out
the high temperature fried the inside of the connector, and we had to purchase a new
cable and filament. Replacing the burnt one required bringing the chamber up to
pressure, thus, bake out number two, which was conducted in a similar fashion. For
both of these bake outs we had a quartz window sealed with a gold gasket in place
of the Hellma cell. Once we installed the Hellma cell with the lead gasket, we baked
out for a third and (supposedly) final time. However, the power went out briefly near
the end of the bake out and partially vented the chamber, requiring a fourth, brief
bake out. Our meticulous work paid off, as we achieved a pressure .10−10 torr on
the low-pressure side of the chamber. We crushed the rubidium ampoule after all the
baking was complete.
2.5. The Dipole-Trap Laser
In our experiment we employ a single-beam, optical dipole trap (Section 1.6),
which requires high powers and large detunings from the atomic resonance. Initially,
we tried to form a dipole-trap using light produced by a tapered amplifier designed
and built by Matthias Fuchs [76]. However, the presence of resonant light in the
beam lead to substantial atom loss, impacting its usefulness as a dipole-trap laser.
We attempted to remove the resonant light by placing a rubidium vapor cell in the
64
beam path, but we only met with paltry success. Even with tripling the beam path
through the cell and significant heating of the cell to increase the vapor pressure,
atoms remained visible for no more than 80 − 90 ms in the dipole trap. Eventually,
we abandoned the effort and installed a high-power, Ytterbium-doped fiber laser (SPI
Lasers model SP-M-20-A-1090-N-20-DC) that successfully traps the atoms.
The fiber laser has a wavelength of 1090(5) nm, yielding a detuning of over 300 nm
from the 780 nm D2 line of
87Rb, and a maximum power output of 20 W. The laser
emits an unpolarized, multiple-longitudinal-mode, nearly Gaussian, collimated output
beam with a measured beam waist of 1.9(1) mm (1/e2 intensity radius).
We control the fiber laser with a home-built interface box, which has a manual
on/off switch (the laser cannot be turned on with the computer if this switch is off)
and provides manual or computer control of the output power with the flip of a
switch. A modulation input with digital switching capability provides the computer
control. Three LCD screens display the manual CW set-point, power output and
laser temperature, and the box sports a large, red emergency-shutdown button should
something go catastrophically wrong (Fig. 2.24).
To create a single-beam, optical dipole trap, we focus the beam to a 30.9(5) µm
waist (1/e2 intensity radius) with a 200 mm focal-length lens. We considered several
factors when deciding the focal length, including spherical aberration, beam waist,
and positioning the lens not to be too close to the end of the Hellma cell. The
output collimator and focusing lens are housed in a lens tube that we mounted on
65
Figure 2.24. Picture of the home-built, fiber-laser control box, including several
LCD displays showing the manual CW set-point, power output and laser temperature,
and the emergency stop button.
two translation stages and a precision air-bearing stage (Aerotech model ABL 10100-
LT), allowing for three-dimensional control of the dipole-trap beam. The precision
stage (air cart) has sub-micron accuracy and repeatability, and we are able to control
its position, speed, and acceleration with the computer. This allows us to transport
dipole-trapped atoms from the MOT region of the Hellma cell to other regions that
have improved optical access.
We aligned the dipole-trap beam to pass through the end of the Hellma cell,
intersect the MOT, then reflect from one of the dumping mirrors into a custom-
built beam dump [Fig. 2.25(b)]. We placed a long-focal-length lens after the vacuum
viewport to help the expanding beam fit into the beam-dump entrance. Requiring
the beam to intersect the MOT and the dumping mirror resulted in a beam path that
was not parallel to the table nor to the long axis of the Hellma cell (Fig. 2.25). Since
we aligned the air cart parallel to the Hellma-cell axis, translating the dipole trap
shifted the focus in all three dimensions (as opposed to just axially) and misaligned
the beam with the dumping mirror. Initially, this did not pose a problem, but later
66
Dipole-Trap
Beam Spherical
Cube
MOT
Air Cart
Mirror
Hellma Cell
Side View
(a)
Air Cart
Dipole-Trap
Beam
Hellma Cell
Mirrors
Spherical
Cube
MOT
Top View
(b)
Figure 2.25. Schematic diagram showing the alignment of the dipole-trap beam with
the MOT and the dumping mirrors, including the air cart, dipole-trap beam, Hellma
cell, MOT, spherical cube and dumping mirrors. (a) Side view illustrating the angle
between the dipole-trap beam and the Hellma-cell axis. (b) Top view illustrating
how the dipole-trap beam is not parallel to the air-cart-translation direction and the
Hellma-cell axis.
we had to change the air cart position and the beam height for the one-way-barrier
cooling experiment, which required translating the atoms in the dipole trap.
To overlap the dipole-trap laser with the MOT, we aligned a resonant beam first,
then overlapped the dipole-trap beam with the path of the resonant beam using two
irises. The resonant beam easily blows the MOT atoms away without being very
centered on it, making the initial alignment fairly simple. The dipole-trap beam, on
the other hand, must be very near the MOT to have a visible effect due to its large
67
detuning. Once the dipole-trap beam is near the MOT, we use the translation stages
and/or the magnetic fields (from the Helmholtz coils) to improve the overlap, looking
for the position where the dipole-trap beam most greatly affects the MOT.
2.6. Imaging System
We image the atoms using a charge-coupled-device (CCD) camera (Finger Lakes
Instruments MicroLine model with KAF-0402ME sensor). Though not ideal for our
work, it sufficed for the duration of the one-way-barrier experiments, with the shutter
posing our most significant challenge. The shutter had a penchant for sticking and
wore down quickly with repeated use, requiring frequent cleaning and repair.
We placed the camera perpendicular to the dipole-trap axis (Fig. 2.26), and affixed
a manual lens (Nikon Micro-Nikkor 55mm f/3.5, purchased used) on the camera to
focus the light onto the CCD. In an effort to reduce unwanted light from reaching
the CCD, we installed a combination of a laser-line filter (Semrock P/N LL01-780-
11.9-D) and AR-coated RG715 Schott glass (Newport Industrial Glass RG 715, AR
coated by CVI) in between the lens and the CCD. The laser-line filter only passed
780 nm light until ∼575 nm, at which point it became highly transmissive at shorter
wavelengths. To remedy this, we added the Schott glass to remove any light with a
wavelength shorter than 575 nm. Later we removed the laser-line filter as it produced
significant, non-stationary fringes in our images (the Schott glass blocks light with
68
Absorption
Imaging Beam
CCD 
Camera
Dipole-Trap
Beam
11
repump beam power (mW)
p
op
u
la
ti
on
 (
n
or
m
al
iz
ed
)
Transmitting side
0.001 0.01 0.1 1 10
0
0.2
0.4
0.6
0.8
1.0
left
right
total
no barrier, left
no barrier, right
Reflecting side
0.001 0.01 0.1 1 10
0
0.2
0.4
0.6
0.8
1.0
left
right
total
no barrier, left
no barrier, right
FIG. 10: (Color online) Populations on the left- and right-hand sides of the one-way barrier after 100 ms as functions of
repumping-barrier-beam power. The left panel shows results where the atoms were initially on the left-hand (transmitting)
side of the barrier, and the right panel shows results where the atoms were initially on the right-hand (reflecting) side. The
vertical lines in the plots show our usual repumping-barrier-beam power of 0.36 µW. The two horizontal bars show the ending
populations from data taken with no barriers [the one shown in column (a) of Fig. 4 and a similar data set where atoms
were initially on the other side of the barrier]. The no-barrier cases show unequal left- and right-hand populations due to the
oscillations of the atoms. Error bars indicate statistical error from at least 38 repetitions.
time (ms)
p
op
u
la
ti
on
 (
n
or
m
al
iz
ed
)
Transmitting side
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1.0
left
right
total
Reflecting side
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1.0
left
right
total
Transmitting side (no barrier)
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1.0
left
right
total
Reflecting side (no barrier)
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1.0
left
right
total
FIG. 11: (Color online) Populations on the left- and right-hand sides of the one-way barrier for a few different repumping-
barrier-beam powers as functions of time. The top two panels show data collected without barrier beams. The bottom two
panels are generated from the same data used in Fig. 10. The data with the dotted line and squares correspond to the minimum
beam power (about 2 nW) shown in Fig. 10. The data with the dashed line and diamonds correspond to approximately the
same power used to collect our canonical data. The data with the solid line and triangles correspond to the maximum beam
power (about 9 µW) shown in Fig. 10. The top curve in each panel shows the total population, while the other solid symbols
show the right-hand side population and the open symbols show the left-hand side population.
(a) (b)
left- ide start right-side start
Dipole-Trap
Beam
Main Barrier
Beam
Repumping
Barrier Beam
Dipole-Trapped
Atoms
Figure 2.26. Schematic diagram showing the orientation of the CCD camera and
absorption-imaging beam relative to the dipole trap.
wavelengths shorter than 700 nm). The entire imaging system (CCD, filter and lens)
has a resolution of 24.4 µm/pixel.
We image the atoms using either fluorescence imaging or absorption imaging,
depending on the needs of the experiment. Fluorescence imaging involves collecting
the light emitted by the atoms when they are illuminated with the MOT-trapping
beams. This technique is useful for calculating atom numbers and measuring tem-
peratures, but does not have particularly good spatial resolution because the atoms
move noticeably during the time of the illumination pulse. To fluorescence image the
atoms, we typically flash the MOT-trapping and repump beams at he int nsity and
detuning used to form the MOT for 20 ms. The long interaction time ensures a strong
signal for atom-number and temperature calculations de pite the small number toms.
In absorption imaging, a weak, resonant beam illuminates the atoms, such that any
light passing through becomes absorbed. The CCD then images the unabsorbed light,
and the absence of light in the image indicates he location of the atom cloud. This
69
imaging method provides good spatial resolution, but is fairly sensitive to intensity
fluctuations.
We placed our absorption-imaging beam on the other side of the Hellma cell
opposite the camera (Fig. 2.26), and derived the light from the zero-order diffraction
beam produced by the AOM that controls the second-MOT intensity. Since the
absorption-imaging beam and the MOT beams are never on at the same time, using
the same beam for two different functions does not pose a problem. To shift the
zero-order beam to resonance and control its intensity, we pass it through another
80 MHz AOM (Isomet P/N 1205C-1) and then couple it into a fiber. We use a large
output collimator (same as for the six MOT beams) to increase the width of the beam
for imaging, since we need a nearly-uniform intensity over the spatial extent of the
atom cloud. Next, the beam passes through a 2◦ wedge prism placed at 45◦ (Thorlabs
P/N PS810), which reflects about 10% of the beam (Fig. 2.27). The wedge shape
prevents fringes that can result from the surfaces of the prism forming an etalon.
We focus the transmitted beam into our home-built pulse-stabilization circuit, which
integrates the power of each absorption pulse up to a set value to maintain a consistent
integrated intensity (as opposed to pulse length) from one pulse to the next pulse.
The reflected beam illuminates the atoms after passing through an anamorphic prism
pair (×4 magnification) that horizontally expands the beam even further, since the
atoms spread out over a few millimeters in the longitudinal dimension of the dipole
trap. The absorption imaging pulse is typically about 45 µs, and we shift the laser
70
Anamorphic
Prism Pair
Lens
f = 150 mm
Pulse-
Stabilization
Circuit
2˚ Wedge
Prism
Fiber
Collimator
To Hellma Cell
AOM
Mirror 1 Beam
Splitter
Lens
f = 250 mm
Mirror 2 To
Hellma
Cell
(x6)
Small Optics Table
Main 
Barrier 
Beam
Repumping 
Barrier
Beam
Fiber
Collimators
Figure 2.27. Schematic diagram of the absorption-imaging optics showing the AOM,
fiber-output collimator, 2◦ wedge prism, anamorphic prism pair, lens, and pulse-
stabilization circuit.
frequency very close to the F = 2 → F ′ = 3 resonance. We also include a repump
pulse (with the second MOT beams) to ensure all atoms atoms are in the F = 2
hyperfine ground state.
In addition to the data camera, we have two Sony video cameras (Supercircuits
P/N SSC-M383), typically used in security applications, that monitor the pyramid
MOT and the second MOT. These cameras are equipped with a 6× zoom lens
[Edmund Optics NT52-274 (discontinued)], and we monitor the output on small LCD
monitors. These cameras provide us an easy way to verify the MOT(s) are working,
and play a critical role in overlapping the MOT and the dipole trap.
71
2.7. Control and Timing Electronics
Our entire experiment is computer controlled (except for locking the lasers and
overlapping the MOT and the dipole trap) using an open-source, home-built system,
affectionately referred to as ZOINKS (Zee Open Interface Networked Kontrol System)
[77]. This system was designed to eliminate the need for expensive proprietary
software and hardware, providing a versatile and easy-to-construct system for con-
trolling atom-optics experiments. The main idea is to connect one control computer to
several micro-processors, which then communicate with interface boards that control
multiple digital- and analog-output channels. These channels control the various
pieces of equipment in our experiment, such as the CCD camera, shutters, AOMs,
and magnetic coils. The desired timing and control sequence is set in a Perl script
executed by the user at the control computer, using an extensive library of Perl
modules and subroutines designed specifically for our experiment by Jeremy Thorn.
The control computer sends this information via ethernet to the microprocessors,
which then pass the information to the interface boards that precisely execute the
sequence. The interface boards are synchronized to a 10 MHz atomic clock and
provide timing accurate to 0.02 µs with a 4 µs resolution. This system has allowed
us to control virtually all aspects of our experiment with precision timing, greatly
simplifying various alignment procedures, troubleshooting, and data collection.
72
CHAPTER III
THE ONE-WAY BARRIER PART I: THE MECHANICS
Figure 3.7 was published in the coauthored work, Ref. [78].
3.1. Introduction
The field of atom optics has catapulted to the forefront of physics research as a
result of its success at controlling and manipulating the motional states of atoms, and
it continually strives to develop new and more broadly applicable methods. The “one-
way barrier,” or “atom diode” [78–90] is a welcome addition to its arsenal, as it can
be implemented with a wide range of atomic and molecular species. Additionally, this
new control tool has potential application in emerging cold-atom technologies such as
atom chips [91, 92]. Proposed independently by Raizen et al. [79] and Ruschhaupt
and Muga [80], the one-way barrier, composed of two laser beams, allows atoms
traveling in one direction to pass through, but reflects atoms traveling in the other
direction. In this chapter we will discuss the concept of the all-optical one-way barrier,
its relation to Maxwell’s Demon, and our experimental implementation of the barrier
[78, 90].
73
(a)
(c)
(b)
1
2
3
Figure 3.1. Energy level structure for the three-level atom with two ground states
and one excited state used to introduce the concept of the one-way barrier.
3.2. How It Works
We will explain the concept of the one-way barrier in the context of the three-
level atom shown in Figure 3.1, which has two ground states and one excited state,
though it potentially has broad application to almost any level configuration given
careful consideration of the atomic structure and laser frequencies. Several schemes
for different two- and three-level systems have been outlined by the original authors
[79, 80], and Thorn et al. [78] outlines a possible scheme for a four-level system.
The optical dipole potential, discussed in Section 1.6, embodies the main physics
involved in the one-way barrier. In this phenomenon, the ac electric field of a
non-resonant laser beam interacting with an atom shifts the atom’s energy levels
proportional to I/∆. Here, I is the laser intensity and ∆ = ω − ω0 is the laser
detuning, defined as the difference between the laser frequency ω and the atom’s
resonance frequency ω0. The intensity profile of the laser beam dictates the magnitude
of the shift, while the sign of the detuning determines the direction of the shift, and
74
thus the nature of the resulting potential. For example, a focused, Gaussian laser
beam with a negative detuning (red-detuned) presents an attractive potential to the
atom, centered on the position of the focus, while a positively-detuned laser beam
(blue-detuned) presents a repulsive potential (Section 1.6).
To create the one-way barrier for the three-level atom, we start by tuning the
frequency of a laser beam part way between the two resonant frequencies for states
|1〉 and |2〉 [Fig. 3.2(a)]. For this frequency, an atom that encounters the laser
beam in state |1〉 will see an attractive potential and pass through, while an atom
in state |2〉 will see a repulsive potential and reflect [Fig. 3.2(b)]. To make the
barrier unidirectional, we add a second laser beam, positioned to the right of the
first [Fig. 3.2(c)], that is resonant with the transition from state |1〉 → |3〉. We refer
to the first beam as the main barrier beam and the second beam as the repumping
barrier beam. In this configuration, we start the atoms in state |1〉 (the transmitting
state), such that atoms impinging on the barrier from the left-hand side see an
attractive potential and pass through unimpeded. After transmitting through the
main barrier beam, the repumping barrier beam immediately optically pumps the
atoms to state |2〉. Once in state |2〉 (the reflecting state), the main barrier beam
presents a repulsive potential and the atoms reflect from it. Atoms starting on the
right-hand side of the barrier get optically pumped to the reflecting state by the
repumping barrier beam before encountering the main barrier beam, ensuring they
reflect from it and remain on the right-hand side. The operation of the barrier is
75
Main Barrier 
Beam
1
2
3
Barrier Basics:
Setup
We start atoms in the transmitting state, and have a
second beam pump them into the reflecting state on one
side.
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BarrierBasics:
Setup
Westartatomsinthetransmittingstate,andhavea
secondbeampumpthemintothereflectingstateonone
side.
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Barrier Basics:
Setup
We start atoms in the transmitting state, and have a
second beam pump them i to t e reflecting state on one
si e.
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(a) (b)
Main Barrier 
Beam
3
1
2
Barrier Basics:
Setup
We start atoms in the transmitting state, and have a
second beam pump them into the reflecting state on one
side.
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Barrier Basics:
Setup
We start atoms in the transmitting state, and have a
second beam pump them into the reflecting state on one
side.
Powered by LATEX – p. 6/9
Barrier asics:
Setup
We start ato s in t transmitting state, and have a
second beam pump them into the reflecting state on one
side.
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Repumping 
Barrier Beam
(c) (d)
One-Way Barrier
Reflecting
Transmitting
Reflecting
Transmitting
Figure 3.2. Schematic diagram illustrating different aspects of the one-way barrier.
(a) The detuning of the main barrier beam relative to the transmitting and reflecting
states. (b) Atoms in the red-detuned state (state |1〉) will pass through the barrier,
while atoms in the blue-detuned state (state |2〉) will reflect fro it. (c) The frequency
of the main barrier beam and the repumping arri r beam for the three-level atom.
(d) Atoms approaching the barrier from the left in the transmitting state will pass
through, where the repumping barrier beam optically pumps them to the reflecting
state.
illustrated schematically in Figure 3.2(d). In the remaining chapters, the left side of
the barrier will always correspond to the transmitting side, while the right side will
correspond to the reflecting side.
76
3.3. Maxwell’s Demon
Beyond its potential as a tool for controlling the motion of atoms, the one-way
barrier is intrinsically fascinating as a physical realization of Maxwell’s demon [78,
85, 90]. In 1871, Maxwell pondered a paradox, positing a creature capable of making
heat flow from cold to hot without performing any work, a violation of the second
law of thermodynamics [93–95]. He imagined a container filled with gas particles,
partitioned by a wall containing a trap door. A small creature operated this trap
door, opening it to allow warmer particles to travel to the right-hand side of the
container and cooler ones to travel to the left-hand side, but closing it to prevent
them from passing back through. The creature, later referred to as Maxwell’s demon,
thus creates a flow of heat from cold to hot, generating a temperature differential
where previously the system had been in equilibrium. Intuitively, we know this is
only possible if energy (in the form of work) is supplied to create and sustain the
temperature differential, such as the electricity used to run a refrigerator or an air
conditioner. In the case of the demon and its trap door, there appears to be no energy
supplied to the system to create and maintain the temperature gradient, thus creating
the paradox of the demon’s existence and its apparent violation of the second law of
thermodynamics.
The heart of the conundrum lies with the second law of thermodynamics, which
at its most fundamental level states that the entropy of the universe must increase
or remain the same, and is tied to the concept of reversibility. Reversible processes
77
leave the overall entropy of the universe unchanged, so any increase in one system
must be balanced by a decrease elsewhere, while irreversible processes increase the
total entropy of the universe. Entropy provides a measure of the number of states
accessible to that system, expressed as S = kB ln g, where kB is the Boltzmann factor,
and g is the number of accessible states. Changes in the entropy of that system
are related to its temperature and any heat transfer between it and another system.
When heat flows from a hot system to a cold system, the entropy increase of the cold
system is greater than the corresponding decrease of the hot system, such that the net
effect increases the total entropy of the universe, rendering the process irreversible.
The demon and trap-door system conceived by Maxwell is problematic in that it does
the opposite: separating the warm and cold atoms without performing work requires
a reduction in the overall entropy of the universe, a violation of the second law of
thermodynamics.
A variation of Maxwell’s thought experiment involves the demon operating the
trap door as a one-way barrier, opening it to allow gas particles to travel to the right-
hand side, but closing it to prevent the particles from traveling to the left-hand side,
thereby collecting all the particles on one side of the container (Fig. 3.3). Though this
version does not involve temperature gradients, the entropic nature of the paradox
remains the same. The system depicted in Figure 3.3 is isolated, such that no heat can
be transfered to or from its surroundings, and any change it undergoes is described
as adiabatic. Reversible, adiabatic processes occur at constant entropy (∆S = 0),
78
poor 
reflection
poor 
reflection
poor 
reflection
excellent
reflection
excellent
reflection
better 
reflection
z1 y1
z2 y2
z3 y3
barrier out of focus
barrier near the focus
barrier at the focus
barrier too high
barrier too low
barrier centered
(a) (b)
Depth-of-Focus Alignment Vertical Alignment
Figure 3.3. Illustration of the one-way barrier compressing the volume of a sample
of gas, modified from an original created by J.J. Thorn.
since any change in entropy is intimately tied to the transfer of heat, which does not
occur in an adiabatic process. During reversible, adiabatic compression (such as that
performed by the demon), the reduction in volume is accompanied by a rise in the
temperature, such that any decrease in entropy from the reduced volume is exactly
balanced by the increase in entropy from the higher temperature. But herein lies the
rub: studying the demon and trap door system, we see no increase in temperature—
the speed of the particles has not increased—yet the volume has definitely been
reduced. However, no work has been performed to carry out this reduction in volume
either. There is no obvious increase in entropy elsewhere in the system to balance
the decrease involved in compressing the volume. So the question remains: how do
we reconcile Maxwell’s demon and the second law of thermodynamics?
The answer to this question emerged over a century later, resulting from work
on the thermodynamic implications of information storage and disposal in context
of computing [94, 95]. Of particular importance is the concept that erasing stored
information, such as the bits making up a computer’s memory, is a thermodynamically
79
irreversible process that dumps entropy into the environment surrounding the device.
The connection to Maxwell’s demon lies within the fact that the demon must make
a measurement on, and thus gain information about, each gas particle as it whizzes
toward the trap door. If it has one bit of memory, after determining which side of
the container the particle is on, its memory has two possible states—“on the left-
hand side” or “on the right-hand side”—which yields an entropy of kB ln 2. Before
it can observe the next particle, its memory must be reset, which reduces the two
possible states to one possible state—“the reset state”—which has zero entropy. To
compensate for the reduction in entropy of the demon’s memory, the corresponding
amount of entropy must be dumped to the environment during the resetting process
to guarantee compliance with the second law.
More realistically, assume the demon’s memory has just enough storage space to
retain position information about all N gas particles, and starts in the state where
each bit is set to “on the left-hand side.” This initial state has zero entropy since
there is only one possible configuration of bits that produces this state. Assuming
the particles have an equal probability of residing in the left-hand or right-hand side
of the container, the demon’s memory will be in one of the 2N possible states after
measuring all N particles, resulting in an entropy increase of NkB ln 2. We calculate
the corresponding entropy decrease experienced by the gas particles by considering the
entropy difference between the 2N possible ways to distribute N particles between the
two sides of the container, and the one possible way to distribute the atoms when they
80
all reside in one side of the container. This calculation shows an entropy decrease
of NkB ln 2, which is the exact amount by which the demon’s memory increases,
and the exact amount that would be dumped to the surrounding environment if the
demon’s memory is erased. Neither of these situations violate the second law of
thermodynamics, so the demon and the laws of physics are able to coexist.
In reality, the experiment has several sources of heat and entropy that arise during
the compression process, including photon recoil, unwanted scattering events, laser
beam jitter, random spontaneous emission directions, and frequency changes in the
scattered repumping-barrier-beam photons due to the switching process. Interestingly
though, we can ignore all of these contributions except the last one, and entirely
balance the entropy decrease of the atoms solely by examining the entropy increase
of the repumping barrier beam due to frequency changes during the trapping process.
The frequency changes arise from the slight energy difference between the transmitting
and reflecting states, because every atom that becomes trapped by the barrier must
absorb a repumping-barrier-beam photon that is resonant with the |1〉 → |3〉 tran-
sition, while the photon emitted back into the repumping barrier beam has a lower
frequency, as it is resonant with the |2〉 → |3〉 transition. As a result, studying the
frequency of the repumping-barrier-beam photons provides a record of the number
of atoms trapped by the barrier, while each photon produced by the irreversible
state change each atom undergoes during the switching process carries away the
entropy necessary to balance any decrease experienced by the atom during the process.
81
Mathematical expressions for the change in entropy of the atoms and the repumping
barrier beam during the trapping process have been derived in Thorn et al. [78], and
in the large-atom-number approximation it has been shown that the entropy increase
of the repumping barrier beam is at least as large as the corresponding decrease in
the atoms’ entropy, thus ensuring compliance with the second law of thermodynamics
[78].
3.4. Implementation
We realize the all-optical one-way barrier with 87Rb atoms using the D2 transition
(Fig. 2.4), which has hyperfine structure (Fig. 3.4) very similar to the three-level
atom described above. In this case, the F = 1 and F = 2 hyperfine ground
levels correspond to states |1〉 and |2〉 respectively, while the F ′ hyperfine manifold
effectively corresponds to state |3〉 due to the small hyperfine shifts. We generate the
main barrier beam by locking a third master laser to the largest spectral feature in the
85Rb F = 3→ F ′ saturated-absorption spectrum, which conveniently lies in between
the two 87Rb hyperfine transitions (Fig. 3.5). Using the 85Rb transition provides
an opportune way for us to obtain a stable laser frequency with an appropriate
detuning for each ground state because we already have its saturated-absorption
spectrum due to the presence of both isotopes in our vapor cells. Stabilizing the
main-barrier-beam laser to this transition (the F = 3→ F ′ = 3, 4 crossover) yields a
82
Main Barrier 
Beam
5  S2 1/2
5  P2 3/2
780 nm
(384 THz)
F=1
F=2
F!=0
F!=3
..
.
6.8 GHz
0.5 GHz
F=1
F=2
F!=0
F!=3
..
.
1.05(5) GHz
Repumping 
Barrier Beam
Mirror Mount
Vertical- 
Adjustment 
Screw
Horizontal- 
Adjustment Screw
STM Tip
Knob
Colored 
Grooves
Black 
Ridges
Rb87 D2 line
Rb87 D2 line hyperfine structure 
Figure 3.4. Hyperfine structure for the 87Rb D2 transition showing the relevant laser
frequencies for the main barrier beam and the repumping barrier beam.
detuning 1.05(5) GHz blue of the 87Rb MOT-trapping transition (Fig. 3.4). We lock
the repumping barrier beam to the 87Rb F = 1→ F ′ = 2 repump transition.
Initially, we stabilized the main barrier beam to the 85Rb F = 2 → F ′ = 2
transition, which appeared t be an obvious choice since it lies nearly halfway in
between the 87Rb F = 1 and F = 2 hyperfine transitions (Fig. 3.5). This choice
of detuning, however, created a poorly performing one-way barrier, because atoms
in the F = 1 state still scattered a significant amount of main-barrier-beam photons
during transmission. As a result, atoms traversing the barrier in the F = 1 state were
frequently pumped to the F = 2 state, at which point the main barrier beam presented
a very strong, repulsive potential, imparting a substantial amount of kinetic energy to
the atoms. Unwanted heating during transmission, and thus the performance of the
barrier, improved significantly by choosing a frequency further red-detuned from the
83
probe wavelength
p
ro
b
e
 t
ra
n
s
m
is
s
io
n
(F=2       F!)
Rb87
repump
transition
MOT
transition
Rb85
F=3       F!
(F=1       F!)
F=2       F!
Figure 3.5. Saturated-absorption spectrum for the rubidium D2 transition showing
the relative frequencies for the 85Rb and 87Rb isotopes. This figure is modified from
an original provided by D.A. Steck.
F = 1 ground state. Fortunately, the 85Rb F = 3 → F ′ = 3, 4 crossover transition
proved to be an effective choice for the main-barrier-beam frequency, allowing us to
avoid implementing a separate frequency stabilization scheme. We will discuss the
topic of scattering and the main-barrier-beam frequency in more depth in Section 4.4.
In order to demonstrate the one-way barrier, we need to restrict the atoms to a
region of space containing the barrier. We accomplish this by confining the atoms
in the single-beam optical dipole trap described in Section 2.5, and intersecting its
focus nearly perpendicularly with the barrier beams (Fig. 3.6). The 12(3)◦ angle
between the barrier beams and the dipole trap’s perpendicular allows optical access
84
Absorption
Imaging Beam
CCD 
Camera
Dipole-Trap
Beam
11
repump beam power (mW)
p
op
u
la
ti
on
 (
n
or
m
al
iz
ed
)
Transmitting side
0.001 0.01 0.1 1 10
0
0.2
0.4
0.6
0.8
1.0
left
right
total
no barrier, left
no barrier, right
Reflecting side
0.001 0.01 0.1 1 10
0
0.2
0.4
0.6
0.8
1.0
left
right
total
no barrier, left
no barrier, right
FIG. 10: (Color online) Populations on the left- and right-hand sides of the one-way barrier after 100 ms as functions of
repumping-barrier-beam power. The left panel shows results where the atoms were initially on the left-hand (transmitting)
side of the barrier, and the right panel shows results where the atoms were initially on the right-hand (reflecting) side. The
vertical lines in the plots show our usual repumping-barrier-beam power of 0.36 µW. The two horizontal bars show the ending
populations from data taken with no barriers [the one shown in column (a) of Fig. 4 and a similar data set where atoms
were initially on the other side of the barrier]. The no-barrier cases show unequal left- and right-hand populations due to the
oscillations of the atoms. Error bars indicate statistical error from at least 38 repetitions.
time (ms)
p
op
u
la
ti
on
 (
n
or
m
al
iz
ed
)
Transmitting side
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1.0
left
right
total
Reflecting side
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1.0
left
right
total
Transmitting side (no barrier)
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1.0
left
right
total
Reflecting side (no barrier)
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1.0
left
right
total
FIG. 11: (Color online) Populations on the left- and right-hand sides of the one-way barrier for a few different repumping-
barrier-beam powers as functions of time. The top two panels show data collected without barrier beams. The bottom two
panels are generated from the same data used in Fig. 10. The data with the dotted line and squares correspond to the minimum
beam power (about 2 nW) shown in Fig. 10. The data with the dashed line and diamonds correspond to approximately the
same power used to collect our canonical data. The data with the solid line and triangles correspond to the maximum beam
power (about 9 µW) shown in Fig. 10. The top curve in each panel shows the total population, while the other solid symbols
show the right-hand side population and the open symbols show the left-hand side population.
(a) (b)
left- ide start right-side start
Dipole-Trap
Beam
Main Barrier
Beam
Repumping
Barrier Beam
Dipole-Trapped
Atoms
Figure 3.6. Schematic diagram illustrating the orientation of the barrier beams
relative to the dipole-trap axis and focus. This figure was adapted from an original
created by J. J. Thorn. 3
-1 0 1
-14
-16
-18
-20
distance (mm)
p
ot
en
ti
al
 (
M
H
z)
reflecting 
 transmitting
   dipole-trap potential
FIG. 3: (Color online) Optical potentials seen by atoms along
the axis of the dipole trap in our experiment. The overall trap-
ping potential is from the main dipole-trap beam, while the
narrow state-dependent feature results from the main barrier
beam. Th main barrier beam produces a repulsive potential
for atoms in the reflecting (F=2) grou state, and an at-
tractive tential for atoms in he transmitting (F=1) ground
state.
to atoms in the F=1 ground state and a repulsive po-
tential to atoms in the F=2 ground state, because the
optical dipole potential is inversely proportional to the
detuning ∆. These two potentials are plotted in Fig. 3.
To create the asymmetry, we introduce a second beam,
the repumping barrier beam, that is resonant with the
F=1 → F ′=2 repumping transition, displaced from the
main barrier beam as shown in Fig. 1. If all atoms start
in the transmitting (F=1) ground state, they can pass
through the main barrier beam until they pass through
the repumping barrier beam, at which point they will be
pumped to the reflecting (F=2) ground state. The atoms
will then see the main barrier beam as a potential bar-
rier and will remain trapped on that side of the one-way
barrier. We choose to have the repumping barrier beam
on the right-hand side of the main barrier beam, which
makes that side the reflecting side of the barrier, and the
left-hand side the transmitting side.
We initially cool and trap the 87Rb atoms in a standard
six-beam magneto-optic trap (MOT) [21], loaded from a
cold atomic beam produced by a pyramid MOT [26]. Af-
ter a secondary polarization-gradient cooling stage with
reduced intensity and increased detuning of the trapping
beam, we have about 2 × 105 atoms at about 30 µK in
an ultra-high vacuum of <∼ 10−10 torr. The position of
the MOT can be shifted several millimeters in each co-
ordinate using magnetic bias fields.
After cooling we load the atoms into a far-detuned op-
tical dipole trap pro uc d by a 1090(5) nm Yb:fiber laser.
The laser emits a collimated, multiple-longitudinal-mode,
unpolarized, nearly Gaussian beam with a 1.9(1) mm
1/e2 beam radius. We operate this laser so that the total
power inside the vacuum chamber is 9.3(5) W. We focus
the beam with a single 200 mm focal length plano-convex
lens, producing a 30.9(5) µm waist (1/e2 intensity radius)
and a 2.8 mm Rayleigh length. For 87Rb atoms in either
hyperfine ground state, this beam yields a nearly con-
servative potential well with a maximum potential depth
of k
B
× 0.9 mK. This dipole trap has longitudinal and
transverse harmonic frequencies of 24 Hz and 3.0 kHz,
respectively (near the trap center), a 1/e lifetime of 20 s,
and a maximum scattering rate of only 3 s−1. Atoms are
typically loaded in the anharmonic region of the trap,
so that the atomic motion dephases and has a different
period (50 ms) than the harmonic frequency suggests (an-
gular momentum adds to this effect; see Appendix C).
The two one-way barrier beams are nearly parallel
asymmetric Gaussian beams with a variable separation.
Their foci nearly coincide with the focus of the dipole-
trap beam, intersecting it at about 12(3)◦ from the per-
pendicular to the beam axis (as in Fig. 1). The main
[repumping] barrier beam has a waist of 11.5(5) µm
[13(2) µm] along the dipole-trap axis and 80(7) µm
[60(7) µm] perpendicular to the dipole-trap axis. We
control the power of the repumping barrier beam with
an acousto-optic modulator (AOM).
We measure the separation of the two beams on a beam
profiler that has a resolution of 5.6 µm/pixel. We take
pictures of each beam profile at many locations along the
beam axis near the focus, thus making it possible to ac-
curately locate the axial position of the focus despite the
fact the beam waists are on the same order of magnitude
as the camera resolution. Using this setup, we determine
the separation of the beams (on the order of ten microns)
with an error on the order of a micron.
We image the atoms by illuminating them with a 45 µs
pulse of light resonant with the F=2→ F ′=3 MOT trap-
ping transition. This absorption-imaging beam is nearly
perpendicular to the dipole-trap beam, and is detected
by a charge-coupled-device (CCD) camera, which images
the shadow left by the atoms that scatter light out of
the beam. We image atoms in the F=1 ground state
(which do not scatter the MOT trapping light) by turn-
ing the MOT repumping beams on slightly before and
throughout the imaging pulse, ensuring that all atoms
are in the F=2 ground state. The short image pulse is
ideal for getting accurate spatial imaging, since the atoms
cannot move much during that time. To reduce system-
atic errors due to interference fringes in the images, we
subtract background offsets (as computed from the edge
regions of the images) on a per-column basis and then
integrate each column to form distributions (such as the
ones shown in Fig. 4). The spatial resolution is 24.4 µm
as set by the CCD pixel spacing, but the distributions
are smoothed slightly for visual clarity. The total num-
ber of trapped atoms drifted slowly over time, so we often
rescaled atom distributions in order to aid comparison of
different data sets.
Our “canonical” data are taken as follows. We load the
dipole trap with the MOT centered on the dipole-beam
axis 0.95(5) mm away from the dipole-trap focus for 5 ms,
trapping about 3× 104 atoms (measured by imaging the
resonance fluorescence from the MOT light on a CCD
camera) at ∼100 µK, with a peak one-dimensional atom
density of around 4 × 104 atoms/mm (on the order of
107 atoms/mm3). Longer load times trap more atoms,
but the atoms spread throughout the trap during load-
ing. We used a relatively short loading time to keep the
Figure 3.7. Optical potentials experienced by the atoms along the dipole-trap
axis due to the dipole-trap beam and the main barrier beam. The wide, shallow
potential results from the dipole-trap beam, while the narrow, attractive and repulsive
potentials in th center result from the main barri r beam. The a tractive (repulsive)
potential corresponds that se n by the atoms in the tr nsmitting (reflecting) state.
This figure was created by J. J. Thorn.
for the absorption imaging beam. Since the dipole trap tightly confines the atoms
i the radial direction, we have an effectively on -dimensional, nearly harmonic trap
divided by the one-way barrier. The optical potentials generated by the dipole-trap
beam and the main barrier beam are shown in Figure 3.7.
85
Several factors (beyond the detuning of the main barrier beam) play an important
role in the barrier’s performance, including the size, separation, and power of the
barrier beams. The size requirements of the beams deserve careful consideration in
that we need the beams to span the width of the dipole-trap beam at its focus, yet
we also want them as narrow as possible along the dipole-trap axis (Fig. 3.6). It
is important to have the beams as small as possible along the dipole-trap axis to
decrease the time it takes for an atom to traverse them, which reduces unwanted
scattering events that lead to heating and trap losses. The combination of the two
size requirements led us to use elliptically-shaped barrier beams. The separation of
the two barrier beams also requires some thought. Too much overlap leads to optical
pumping of the atoms to the reflective state while still in the presence of the main
barrier beam, while too much separation may prevent the atoms from switching to
the reflecting state before turning around and heading back towards the barrier (since
the atoms are attracted to the focus where the barrier is located). Initially, we set
the separation such that the Gaussian tails of the barrier beams overlapped slightly,
with the centers almost three beam waists apart. The main barrier beam does not
require a significant amount of power because we focus it to a narrow waist and the
potential barrier it forms only needs to be higher than the kinetic energy of the dipole-
trapped atoms. The repumping barrier beam requires even less power since only a
few scattering events are necessary to optically pump the atoms to the reflecting state
(see Section 3.5 for these parameter values).
86
We oriented the linear polarization of the main barrier beam and repumping
barrier beam parallel and perpendicular to the longitudinal axis of the dipole trap,
respectively. We set the barrier-beam polarizations orthogonal to each other originally
because we initially combined the beams with a polarizing beam splitter cube, but
later switched to a standard beam splitting cube. We later changed the polarizations
to match and observed its effect on the performance of the one-way barrier (see
Section 4.6).
3.5. Optical Setup
As mentioned above, we used a third master laser, equipped with a saturated-
absorption-spectroscopy setup, to generate the light for the main barrier beam. Since
the power requirements of the main barrier beam are not very stringent, we coupled
the remaining light not used in the saturated-absorption setup directly into a fiber for
use in the experiment. We placed a home-built shutter, constructed from a speaker
coil [96], and several neutral density filters in front of the fiber input that enabled us
to turn the barrier beam on and off and control its power, respectively.
Obtaining the repumping-barrier-beam light was more complicated, as we derived
the beam from the master laser that produces the repump light for the MOT setup.
To accomplish this, we picked off the zero-order diffraction beam from the AOM in the
repump setup and immediately fiber coupled it due to space constraints on the table.
We still needed to shift the frequency to achieve resonance with the F = 1→ F ′ = 2
87
repump transition, so we used the fiber to transport the beam to a more spacious
location on the table, where we passed it through an 80 MHz AOM (Isomet P/N
1205C-1) and back into another fiber. Since the repumping barrier beam does not
require a lot of power, losses from the AOM and multiple fiber couplings did not
pose a problem. We also used the AOM to attenuate the intensity of the repumping
barrier beam further. Using the repump-laser light for both the MOT and barrier
setups works well because we typically do not operate the MOT and the barrier at
the same time.
We constructed the optical setup for the barrier beams on a small, 6′′ × 12′′
optical breadboard mounted on 4′′ legs that had several advantages over using the
main optical table. First, it allowed us to align and characterize the barrier beams
elsewhere before inserting them near the Hellma cell, which limits our optical access.
Second, it enabled us to use much shorter optical mounts, thereby improving stability,
since the dipole-trap beam is located about 7.5′′ above the main optical table. Third,
it played a crucial role in overlapping the dipole-trap focus with the foci of the barrier
beams by allowing us to move the foci of the barrier beams without having to adjust
the individual optics, but by simply moving the whole table. Despite these benefits,
we encountered some drawbacks as well, which we will discuss shortly.
The optical layout of the small table is shown in Figure 3.8. We combine the
beams on a 50 − 50 beam splitter cube (Newport P/N 10BC17MB.2), then send
them through a 6× magnification anamorphic prism pair to increase the beam width
88
Anamorphic
Prism Pair
Lens
f = 150 mm
Pulse-
Stabilization
Circuit
2˚ Wedge
Prism
Fiber
Collimator
To Hellma Cell
AOM
Mirror 1 Beam
Splitter
Lens
f = 250 mm
Mirror 2 To
Hellma
Cell
(x6)
Small Optics Table
Main 
Barrier 
Beam
Repumping 
Barrier
Beam
Fiber
Collimators
Figure 3.8. Optical layout for producing and controlling the geometry of the barrier
beams, including the fiber output collimators, critical steering mirrors, beam splitter,
anamorphic prism pair and lens.
in the horizontal direction. Next the beams pass through a 250 mm focal length
lens and reflect from a mirror into the Hellma cell. The main barrier beam focuses
to an 11.5(5) µm waist (1/e2 intensity radius) along the dipole-trap axis and an
80(7) µm waist perpendicular to the dipole-trap axis. The repumping barrier beam
focuses to 13(2) µm nd 60(7) µm waists parallel and perpendicular to the dipole-
trap axis, respectively. The depths of focus for the two beams are slightly different,
which results from imperfect collimation by the fiber collimators, and also explains
the slightly different beam waists (we actually positioned and glued the plugs of these
collimators ourselves, resulting in small variations). The power of the main barrier
beam (inside the Hellma cell) varies depending on the experiment, but it generally
ranges from 24−40 µW of power, while we typically ran the repumping barrier beam
at about 0.35 µW of power (inside the cell).
89
3.6. The Separation of the Barrier Beams
Controlling and measuring a tens-of-microns separation between two laser beams
with about 12 µm waists proved technically challenging, requiring several modifi-
cations to develop a viable method.
Initially, the optical setup did not include mirror 1 (Fig. 3.8), and we attempted
to control the relative height and separation of the two beams by securing the fiber
collimators in the fiber-coupling fixtures (Section 2.3.7), which provided vertical and
horizontal translation and tilt. Unfortunately, these mounts were not very stable,
such that small bumps to the collimators or the fibers permanently altered the beam
positions. Additionally, there was too much coupling between the different degrees
freedom, so we had difficulty independently controlling the vertical alignment and the
horizontal separation. We later secured the fiber collimators in stationary mounts
and added mirror 1, which is our only means of controlling the beam separation and
relative height.
Another challenge involved devising a method to accurately adjust the separation
so we could set it close to a desired value, as we found it difficult to reproducibly turn
the mirror mount knob (New Focus P/N 9773) a small, fixed amount. To remedy
this, we glued an unusable scanning-tunneling-microscope tip (just the small needle)
above the knob and colored every other groove (Fig. 3.9), with the red groove marking
the ideal separation. This allows us to visibly track how many grooves and ridges
we turn the knob each time, and to reliably set the separation to a reasonable value.
90
Main Barrier 
Beam
5  S2 1/2
5  P2 3/2
780 nm
(384 THz)
F=1
F=2
F=0
F=3
..
.
6.8 GHz
0.5 GHz
F=1
F=2
F=0
F=3
..
.
1.05(5) GHz
Repumping 
Barrier Beam
(a) (b)
Mirror Mount
Vertical- 
Adjustment 
Screw
Horizontal- 
Adjustment Screw
STM Tip
Knob
Colored 
Grooves
Black 
Ridges
Rb87 D2 line
Figure 3.9. Illustration of the mirror mount knob used to control the barrier beam
separation, modified to provide visual tracking of how far the knob is turned, including
the mirror mount, knob, scanning-tunneling-microscope tip and colored grooves on
the knob.
We determined that one groove-to-ridge turn (or vice versa) produces about a 4 µm
change in the separation. Typically we operated the barrier with about a 34 µm
separation.
Originally, we set and measured the separation with the small optical table re-
moved from its position near the Hellma cell. To do this, we sent the beams into a
power meter and used a razor blade attached to the air cart to find the center of each
beam. While we were able to accurately measure the separation, moving the small
optical table proved problematic. First, frequently moving the table was a hassle, and
small bumps during the move sometimes shifted the separation and relative height of
the two beams, leaving us unsure of the actual beam geometry during the experiment.
Second, we noticed that simply bolting the legs of the table in place caused it to flex,
significantly affecting the vertical alignment. This led us to develop a method for
91
measuring the beam separation without removing the small optical table from the
experimental setup.
To accomplish this, we placed a mirror in the beam path and reflected the barrier
beams into a beam profiler affixed to a three dimensional translation stage. The beam
profiler consists of a web cam (Panasonic BL-C1, designed for people to observe their
pets remotely) that we modified into a profiler by removing the lens and attaching
neutral density filters. In the spirit of its originally intended use, we refer to it
(as does Panasonic) as the “petcam.” The CCD has a resolution of 5.6 µm/pixel,
which is insufficient to accurately determine the location of each focus (and thus
the separation), since the beam waists are on the same order of magnitude as the
camera resolution. To circumvent this problem, we image each beam profile at several
locations along the beam axis on both sides of the focus, then interpolate to determine
its position.
Generally, we found that the relative height of the barrier beams is very sensitive
and shifts quite a bit over short periods of time, on the order of a week or two. As
a result, we regularly observed the beams on the petcam and visually adjusted for
any vertical shifts using mirror 1. Figure 3.10 illustrates the extent of the vertical
shifts we frequently observed. Since mirror 1 changes the vertical position of the main
barrier beam, it inevitably necessitated realignment of the main barrier beam with
the dipole-trap beam (Section 3.7). We also checked the horizontal separation after
92
Groove
Grabbers
Viewport
Spherical
Cube
Dipole-Trap
Beam
Base
Plate
Mirrors
Grooves
Position
In
te
n
s
it
y
(a)
(b)
(c)
Barrier
Atoms
Dipole Trap
Atomic Distribution
Barrier
Main Barrier 
Beam
Repumping 
Barrier Beam
Petcam Image
Figure 3.10. Depiction of the typical vertical shifts we observed on the petcam for
the relative height of the main barrier beam and repumping barrier beam.
each vertical adjustment because there is a small amount of coupling between the
mirror’s vertical and horizontal degrees of freedom.
3.7. Alignment
One of the more challenging aspects of implementing the one-way barrier was
devising techniques for accurately aligning the focus of the main barrier beam with
the focus of the dipole-trap beam. To set the context, we needed to intersect the
30.9 µm waist of the dipole-trap beam with the 11.5 × 80 µm waist of the elliptical
main barrier beam inside a vacuum cell where we have no physical access. In this
section we will detail the method we finally settled on, though this discussion will not
reflect the continuous refinement of our alignment techniques that led to this method,
necessitated by our quest for a functioning one-way barrier.
We perform this alignment procedure with the repumping barrier beam blocked,
and we assume the relative height and horizontal separation of the two barrier beams
has already been set.
93
time (ms)
ce
n
te
r 
p
o
si
ti
o
n
 (
m
m
)
w
id
th
 (
m
m
)
time (ms)
Dipole-Trap
Beam
Barrier 
Beams
Small Optics 
Table
Mirror 2
Ruler
x
z
y
Dipole-Trap
Beam
Mirror 2
Ruler
Small 
Optics 
Table
x
y
z
Barrier 
Beams
Figure 3.11. Schematic diagram showing the orientation of the x, y, and z alignment
dimensions relative to the dipole-trap axis and barrier beams, including the small
optics table, mirror 2, and the ruler used to measure the table’s position in the z-
direction.
Mirror 2 on the small optical table gives us vertical and horizontal control (the x-
and y-dimensions in Figure 3.11) of the barrier beams, while sliding the small optical
table closer or farther from the Hellma cell changes the z-position. We bolted a rail
with a ruler on top next to the table’s feet so that we could restrict the translation to
the z-dimension and quantify the changes (Fig. 3.11). We generally avoided using the
translation stages that control the dipole-trap-beam position to help with alignment
because we wanted to preserve the dipole trap’s alignment with the MOT and the
dumping mirror, though we did use them to achieve finer adjustments in the z-position
than the sliding-method’s resolution afforded.
We achieve crude alignment of the main barrier beam by overlapping the MOT
with the focus of the dipole-trap beam, and then aiming the main barrier beam where
94
it most greatly affects the MOT. We do this with the main barrier beam tuned (not
locked, just floating) slightly blue of the MOT cycling transition, because at this
detuning small beam powers can blow most of the MOT atoms away. We start with
the small table in a z-position where the main-barrier-beam is out of focus with the
MOT, because the larger beam size aids in the initial overlap of the MOT and the
barrier beam. We steer the barrier beam with mirror 2 until we find the position
where it most greatly affects the MOT. We then incrementally slide the small table
to a z-position near where the main-barrier-beam focus and the MOT overlap, using
mirror 2 to keep the beam aligned on the MOT in the x- and y-dimensions. We know
we are close to the focus when the barrier pokes a small hole in the MOT.
Once we have the main barrier beam and the dipole trap beam in the same vicinity,
we set about precisely adjusting the z-position by looking for the location where the
dipole-trapped atoms best reflect off of the main barrier beam [Fig. 3.12(a)]. To
accomplish this, we increase the power of the main barrier beam and lock it to the
87Rb repump transition because it makes an excellent barrier for atoms in the F = 2
state due to the 6.8 GHz detuning. We then load the atoms away from the center of
the dipole trap and observe how well they reflect off the barrier, then incrementally
change the barrier’s vertical position with mirror 2, looking for the position that has
the best reflection. If we achieve 100% reflection for several vertical positions, we
reduce the power and repeat the procedure. Next we move the z-position of the small
table, and repeat, until we find the z-position that produces the best reflection with
95
poor 
reflection
poor 
reflection
poor 
reflection
excellent
reflection
excellent
reflection
better 
reflection
z1 y1
z2 y2
z3 y3
barrier out of focus
barrier near the focus
barrier at the focus
barrier too high
barrier too low
barrier centered
(a) (b)
Depth-of-Focus Alignment Vertical Alignment
Figure 3.12. Illustration of the reflection-based alignment technique for overlapping
the dipole-trap focus with the blue-detuned barrier-beam focus. (a) The depth of
focus (z-direction) alignment concept, illustrating that an out of focus barrier beam
creates a poorly reflecting barrier. (b) The vertical (y-direction) alignment concept,
depicting how poor vertical alignment of the barrier beam diminishes how well the
barrier reflects atoms.
the lowest power. In our last experiment (Chapter 5) we made finer adjustments to
the z-position using the translation stages that control the dipole-trap position.
We align the vertical position of the barrier using the method outlined above,
finding the y-position of the barrier where the atoms reflect best with the lowest
power [Fig. 3.12(b)]. We set the position of the barrier along the dipole-trap axis
(the x-position) similarly, except we load the trap full of atoms, and then observe
the position where the main barrier beam pokes a hole in the nearly Gaussian atomic
distribution (Fig. 3.13). We use mirror 2 to overlap the main barrier beam with the
peak of the distribution.
96
Groove
Grabbers
Viewport
Spherical
Cube
Dipole-Trap
Beam
Base
Plate
Mirrors
Grooves
Position
In
te
n
s
it
y
(a)
(b)
(c)
Barrier
Atoms
Dipole Trap
Atomic Distribution
Barrier
Main Barrier 
Beam
Repumping 
Barrier Beam
Petcam Image
Figure 3.13. Images demonstrating the horizontal (x-direction) alignment concept
for intersecting the blue-detuned barrier-beam focus with the dipole-trap focus. (a)
Diagram showing the barrier beam misaligned horizontally from the dipole-trap focus.
(b) An actual image the blue-detuned barrier beam poking a hole in the atoms
confined in the dipole trap. (c) The atomic distribution for the average of several
images [like those in (b)], showing the misalignment of the barrier with the dipole-
trap focus.
97
CHAPTER IV
THE ONE-WAY BARRIER PART II: DEMONSTRATION AND
CHARACTERIZATION
Figures 4.5 and 4.7-4.15 were published in the coauthored works, Refs. [78, 90].
4.1. Introduction
Now that we have discussed the mechanics of creating and implementing an all-
optical one-way barrier, in this chapter we will cover the experimental procedures
used to demonstrate successful barrier operation, present our results, and study
its robustness to variations in several of the experimental parameters [78, 90]. In
particular, we will look at how changing the barrier-beam separation, effective barrier
height, repumping-barrier-beam power and main-barrier-beam detuning impact the
barrier’s performance.
4.2. The Dipole Trap
As mentioned perviously, we confine the atoms in a single beam, far off-resonant,
optical dipole trap (Section 3.4), which we focus to a 31.0(5) µm waist (1/e2 intensity
radius) and operate at a power of 9.3(5) W. This produces a nearly conservative,
nearly harmonic trapping potential with axial and radial oscillation frequencies of
98
24 Hz (42 ms period) and 3.0 kHz, respectively. The 2 orders of magnitude difference
between the axial and radial oscillation frequencies allows us to effectively treat the
atomic motion as one-dimensional. For 87Rb in either hyperfine ground state, these
parameters yield a k
B
× 0.9 mK trap depth and a maximum scattering rate of 3 s−1.
We load the atoms into the dipole trap from our six-beam MOT, with the goal
of loading as many atoms as we can at the lowest temperature easily achievable
with our system. To this end, we start by creating a decent-sized, relatively cold
MOT. We typically form the MOT near the center of the Hellma cell, though we
figured out that moving the MOT higher places it near the center of the atomic beam
coming from the pyramid MOT, significantly increasing its size. We accomplish this
by shifting the zero-field position of the anti-Helmholtz coils by increasing the slave-
coil current relative to the master-coil current. We use this trick to our advantage,
shifting the MOT into the atomic beam to bolster its numbers prior to loading the
dipole trap. Once gorged, we implement an additional cooling stage for the MOT
before the loading process. We achieve additional cooling by reducing the intensity
of the MOT trapping light by about 25% and red detuning its frequency further by
another ∼ 54 MHz, implementing a process called “polarization gradient cooling”
[97, 98]. After the polarization-gradient-cooling stage, we have about 2 × 105 atoms
(measured using fluorescence imaging) at a temperature of about 30 µK (measured
using time-of-flight methods).
99
(a)
(c)
(b)
1
2
3
x
z
y
Dipole-Trap
Beam
MOT
Hellma cell
Figure 4.1. Diagram showing the orientation of the x-, y-, and z-dimensions relative
to the dipole-trap-beam.
We use the magnetic bias fields produced by the Helmholtz coils to move the
MOT in the y- and z-dimensions so that it overlaps with the dipole-trap beam for
the loading process (Fig. 4.1). To accomplish this, we turn the dipole-trap beam on
and off at 0.5 Hz, then use the computer to shift the MOT in the y-z plane until
we find the location where the dipole-trap beam has the greatest effect on the MOT.
Due to the large detuning of the dipole-trap beam, we often have to reduce the size
of the MOT to more easily see the effect of the dipole-trap beam. We also had to
check the overlap several times a day during our one-way-barrier experiments as a
yet-to-be-discovered piece of dust on one of the six-beam MOT fiber outputs slowly
shifted the position of the MOT.
The actual loading process involves turning on the MOT and dipole trap simul-
taneously for a period of time (5−110 ms) while overlapping the MOT with the focus
of the dipole trap. Once the MOT-trapping light and magnetic fields are switched
off, the MOT atoms that did not load into the dipole trap rapidly disperse.
100
We use the magnetic bias field in the x-dimension to change the loading position
of the MOT along the dipole-trap axis, which allows us to change the initial kinetic
energy and ensuing dynamics of the atoms. For example, since the dipole trap creates
a nearly harmonic potential, loading in the center generates a symmetric distribution
with little collective motion (possibly a little “breathing”), while loading briefly (∼
5 ms) off to one side produces a small group of atoms that collectively oscillate about
the center of the trap (Fig. 4.2). Loading off to the side for longer periods of time
results in the atoms spreading out spatially to uniformly fill the trap, creating an
atomic distribution that is difficult to distinguish from a center loaded distribution.
Using the bias fields, we can vary the loading position along the dipole-trap axis by
more than 1 mm to either side of the dipole-trap focus.
Initially, we located the axial (x-dimension) position of the dipole-trap focus
relative to the position where the MOT forms by loading the atoms into the dipole
trap and observing their collective motion. We moved the air cart to adjust the
position of the focus until we found the location where the atoms exhibited almost
no oscillatory motion (just breathing) after loading.
Studying Figure 4.2, we see that the actual oscillation period of the atoms is
about 50 ms, which is longer than the 42 ms predicted from the trap parameters
in the harmonic approximation. This discrepancy arises from the both the loading
position of the atoms, which lies in the mildly anharmonic region of the trap, and
angular momentum. In the case of the latter, atoms can acquire a significant amount
101
0 ms
2 ms
4 ms
6 ms
8 ms
10 ms
12 ms
14 ms
16 ms
18 ms
20 ms
22 ms
24 ms
26 ms
28 ms
30 ms
32 ms
34 ms
36 ms
38 ms
40 ms
42 ms
44 ms
46 ms
48 ms
50 ms
52 ms
-3 0 3
position (mm)
ti
m
e
Figure 4.2. Image sequence showing the atomic cloud oscillating about the center
of the dipole trap.
of angular momentum about the dipole-trap axis during the loading process, which
detailed simulations reveal can reduce their axial velocity considerably [78]. Both of
these factors contribute to the atomic cloud’s loss of spatial coherence visible by the
end of the oscillation period.
102
Loading the dipole trap full of atoms (110 ms load time) and taking a fluorescence
image every second, we calculate a 20 s 1/e lifetime for the atoms in the dipole trap.
The long lifetime affords us ample time to perform our experiments.
Once we have successfully loaded the atoms into the dipole trap, we control their
initial hyperfine ground state via optical pumping. To create an ensemble entirely
in the F = 1 ground state, we simply leave the MOT trapping light on for several
milliseconds after loading the atoms into the dipole trap and turning off the repump
light. Reversing the order in which we extinguish the beams produces an ensemble
entirely in the F = 2 ground state. To verify that the optical pumping worked, we
imaged atoms (supposedly) pumped to the F = 2 state with an absorption-imaging
pulse that did not include a repump pulse. Typical optical pumping times range from
7− 15 ms.
4.3. Demonstrating the One-Way Barrier
The procedure for demonstrating the one-way barrier is as follows: First, we
load the atoms into the dipole trap 0.95(5) mm to either side of the focus for 5 ms
(Fig. 4.3), after which we have about 3 × 104 atoms in the dipole trap at about
∼100 µK. Next, we optically pump the atoms into either ground state for 7 ms. We
then let the atoms evolve in the trap for about half an oscillation period (∼20 ms),
after which the atomic ensemble is near its turning point on the opposite side of
trap (Fig. 4.3). We inserted this extra half an oscillation period into the sequence
103
(a) (b)
I
z
z
y
F
za
a
< 0! 
(a)
(b)
(c)
0 2.5-2.5 (mm)
pictures
continue
barrier activated,
pictures begin
half-period
evolution
loading
positiontime
position
MOT
Figure 4.3. Illustration of the one-way barrier demonstration procedure showing the
loading, evolution, and barrier activation sequence.
of events to prevent the dispersing, un-trapped MOT atoms from appearing in the
first few images. The atoms spread out during this half-period delay, reducing their
effective mean displacement from the trap center to 0.65(8) mm (averaged between the
left- and right- start values), despite the initial displacement of 0.95(5) mm (Fig. 4.3).
From this point forward, the initial loading position will refer to the displacement of
the atomic cloud after this half-period delay, such that atoms starting on the left-
hand side of the barrier were actually loaded on the right-hand side of the trap. After
the half-period delay, we turn on the barrier beams (time t = 0 in Figure 4.5) and
take an absorption image of the atoms using an ∼45 µs absorption imaging pulse.
Since each image is destructive, we repeat this procedure, extending the time between
turning the barrier on and taking the image from 0− 100 ms.
104
Dipole-Trap
Beam
Main Barrier
Beam
Repumping
Barrier Beam
Absorption
Imaging Beam
CCD 
Camera
Dipole-Trap
Beam
Main Barrier
Beam
Repumping
Barrier Beam
Absorption
Imaging Beam
CCD 
Camera
Transmitting Side Reflecting Side
Figure 4.4. Schematic diagram showing the optical arrangement identifying the
transmitting (left) and reflecting (right) sides of the one-way barrier, including the
dipole-trap beam, barrier beams, CCD camera and absorption imaging beam. This
figure is a modification of an original diagram created by D. A. Steck.
Figure 4.5 presents our main results for the one-way barrier, showing the dynamics
of the atomic ensemble in response to the one-way barrier. The barrier is located at
the origin of each column, with the main barrier beam positioned to the left of the
repumping barrier beam (Fig. 4.4), identifying the transmitting side as the left-hand
side of the barrier and reflecting side as the right-hand side. To elucidate the effects
of the barrier, Figure 4.5(a) shows the atomic motion in the absence of the barrier,
which simply exhibits the expected oscillatory behavior and loss of spatial coherence
due to the trap anharmonicity and angular momentum.
The data presented in Figure 4.5(b) reveal the atomic evolution in the presence
of the barrier. In this case, the atoms start from the left-hand side of the trap
in the F = 1 transmitting state, such that we expect them to pass through the
105
3
-3 3
position (mm)
0
p
op
u
la
ti
on
 (
ar
b
. 
u
n
it
s)
(a)
0 ms
100 ms
(b) (c) (d)
FIG. 3: Atom spatial distributions along the dipole trap responding to the one-way barrier. The dipole-trap focus and barrier
beams are located at the plot centers. Each image is an average of 78 repetitions of the experiment. Column (a): atoms initially
in F = 1 are dropped from the left with no barrier present. Column (b): atom initially in F = 1 are dropped onto the barrier
from the left (transmitting side). Column (c): atoms initially in F = 2 are dropped onto the barrier from the left. Column (d):
atoms initially in F = 1 are dropped onto the barrier from the right (reflecting side).
the one-way barrier. The atoms begin to the left as in
Fig. 3(a), on the transmitting side of the barrier (that is,
the main barrier beam is to the left and the repumping
barrier beam is to the right in the images). We observe
the atoms transmitting through the barrier on their way
to the right, but when they return, they reflect off the
right-hand side of the barrier. Later, the atomic cloud
settles to a steady state to the right of the barrier.
In Fig. 3(b), atoms started out in the transmitting
F = 1 ground level. But what happens if we repeat
the experiment with atoms in the “wrong,” reflecting
(F = 2) ground level? This situation is shown in
Fig. 3(c), where we see that as expected, many atoms
initially bounce off the barrier, even though they are on
the transmitting side. However, we see that later on, the
atoms still manage to make it through the barrier, with-
out much extra loss. The atoms can do this because we
have chosen the main barrier beam to be more nearly
resonant with the F = 2→ F ′ transitions than with the
F = 1 → F ′ transitions. This beam thus tends to opti-
cally pump atoms into the transmitting F = 1 level. As
discussed below, we chose the barrier detuning to have
this property, which also optimizes the performance of
the barrier in the presence of spontaneous scattering of
barrier photons.
If we drop the atoms from the right-hand (reflecting)
side of the barrier as in Fig. 3(d), we see the atoms reflect
from the barrier. The reflection is clean, even though we
have started the atoms in the “wrong” F = 1 ground
state, because the repumping barrier beam pumps them
to F = 2 before they encounter the main barrier beam.
Of course, we observe similarly good reflections when
0 100
time (ms)
80604020
120
0
p
op
u
la
ti
on
 (
ar
b
. 
u
n
it
s)
100
80
60
40
20
left
right
total
FIG. 4: (Color online.) Populations on left- and right-hand
sides of the one-way barrier, where atoms were initially loaded
throughout the dipole trap, along with the total population.
Error bars indicate statistical error from 38 repetitions.
starting the atoms on the right-hand side in the “proper”
F = 2 state.
Lifetimes on the right-hand side of the barrier typically
range from 300 ms to 500 ms, depending on the temper-
ature of the atoms. At longer times (after warmer atoms
are lost), the lifetimes increase. Fig. 3 (d), at longer time
scales, had a lifetime of > 800 ms. Losses are mainly due
to scattering (and thus heating) from the barrier beams,
both while passing through the main barrier beam and
reflecting from it.
The loss of atoms and optical pumping due to the
main barrier beam point to the main technical challenge
associated with implementing the one-way barrier with
Figur 4.5. A omic distributions in th dipole rap int racting with the barrier,
which is located in the center of each column. Each image is an average of 78
repetitions of the experiment. Colu n (a) Atoms loa d on the left-hand side of
the trap in the F = 1 transmitting state without the barrier. Column (b) Atoms
loaded on the left-hand side of the trap in the F = 1 transmitting with the barrier
present. Column (c) Atoms loaded on the left-hand side of the trap in the F = 2
reflecting state with the barrier present. Column (d) Atoms loaded on the right-hand
side of the trap in the F = 1 transmitting state with the barrier present.
barrier and subsequently become trapped on the right-hand side. We observe the
atoms transmitting through the ba ri r to the right-hand side as expected, turning
around, and then reflecting from the barrier a couple times before reaching a steady
state. How ver, w do not observe a significant number of atoms return to the left-
hand side of the trap, as the barrier successfully obstructs their passage. Figure 4.6
shows the p pulations on both sides f the bar ier as function of time for the same
initial conditions. Again, we see the population on the right-hand side of the barrier
increase and then remain high as the atoms pass through barrier and become tr pped
on its right-hand side. The right- and left-side populations exhibit some oscillation,
106
0 100
time (ms)
80604020
120
0
po
pu
la
ti
on
 (
ar
b.
 u
ni
ts
)
100
80
60
40
20 left
right
total
Figure 4.6. Populations on the left- and right-hand sides of the barrier as function
of time for atoms initially in the F = 1 transmitting state starting on the left-hand
side of the trap. The error bars indicate statistical error for 78 repetitions of the
experiment.
however, indicating that some atoms manage to pass back through the barrier. The
initial population on the right-hand side is not zero because a small portion of the
atomic cloud extends into the right side of the trap when we turn the barrier on at
t = 0.
Figure 4.5(c) shows the resulting dynamics when the atoms begin on the left-hand
side of the trap but in the “wrong” initial state, the F = 2 reflecting state. Under
these conditions, we expect the atoms to reflect from the barrier because it presents
a repulsive potential regardless of the side of incidence. Interestingly though, we
see that while the barrier reflects the atoms initially, they start to transmit to the
right-hand side of the trap despite the barrier (the few atoms visible at t = 0 on the
right-hand side of trap result from the atomic cloud extending beyond the dipole-
107
trap focus when the barrier is activated, rather than atoms transmitting through the
barrier). As the evolution continues, the atoms proceed to slowly leak through the
barrier, such that nearly all of them become confined to the right-hand side of the
trap after 100 ms. We can explain this counterintuitive behavior by recalling that
the main barrier beam is more nearly resonant with the F = 2 → F ′ transition
than the F = 1→ F ′ transition (Section 3.4), resulting in an appreciable amount of
scattering. Atoms in the F = 2 reflecting state that come into contact with the main
barrier beam will initially reflect, however, the barrier will optically pump some of
these atoms to the F = 1 transmitting state during the reflection. These atoms will
then pass through the barrier unimpeded on their next interaction. The main barrier
beam eventually optically pumps all the reflected atoms to the F = 1 transmitting
state during subsequent reflections, allowing the atoms to accumulate on the right-
hand side of the trap. This interesting phenomenon is a direct consequence of choosing
the main-barrier-beam detuning to optimize transmission.
To verify the unidirectional performance of the barrier, Figure 4.5(d) shows the
evolution for atoms initially in the F = 1 transmitting state starting on the right-
hand side of the trap. In this instance, the barrier successfully reflects the atoms
since they encounter the repumping barrier beam first, which optically pumps them
to the F = 2 reflecting state, prior to reaching the main barrier beam. We achieve
comparable reflections for atoms starting in the F = 2 reflecting state.
108
An interesting (and possibly versatile) feature of our one-way barrier is its ability
to transmit atoms approaching from the left-hand side and reflect atoms impinging
from the right-hand side regardless of the atomic state. This feature, which is a direct
result of the 6.8 GHz ground-state hyperfine splitting for 87Rb, potentially broadens
its utility to applications with little or no state control. However, this particular
benefit also comes at a cost, which manifests in the form of increased heating and
trap losses.
4.4. Scattering
The most salient challenge in implementing the one-way barrier results from
the excessive scattering of barrier photons due to the constraints placed on the
main-barrier-beam detuning by the relatively small, 6.8 GHz ground-state hyperfine
splitting of 87Rb. These unwanted scattering events contribute directly to heating via
hyperfine state changes and atom loss due to excited-state, collisional-loss mech-
anisms, beyond the heating expected from the recoil. These processes diminish
trap lifetimes in the presence of the barrier, potentially jeopardizing its wide-spread
applicability.
As mentioned in Section 3.4, tuning the main barrier beam about half way in
between the F = 1 and F = 2 ground states proves to be a flawed (albeit obvious)
choice, as its ability to optically pump a sizeable number of atoms to the F = 2
reflecting state during transmission remains high. An atom that undergoes such a
109
state change while traversing the main barrier beam experiences a sudden increase in
potential energy, resulting in heating on the order of the barrier height. We observed
substantial atom loss during transmission for this choice of detuning, prompting us to
employ an asymmetric detuning much closer to the F = 2→ F ′ hyperfine transition.
We investigate the barrier’s performance for different main-barrier-beam detunings
in Section 4.6.4.
Though the asymmetric detuning significantly reduces devastating state changes
during transmission (as evidenced by our functioning barrier), we reasoned that it
would compromise the barrier’s performance during reflection for the same reason it
improves transmission: The main-barrier-beam frequency is very close to the F =
2 → F ′ hyperfine resonance. Under these conditions, we believed the main barrier
beam would optically pump reflecting atoms (in the F = 2 state) back to the F = 1
transmitting state, allowing them to leak through the barrier (indeed, this is the
same reason our barrier eventually transmits atoms in either state, as discussed in
Section 4.3). This state change (from F = 2 to F = 1), however, does not pose the
same heating problem that the F = 1 to F = 2 state change causes, as the atom’s
potential energy is lowered during the process, reducing the overall energy of the
atom.
To address the anticipated problem of a leaking barrier, we slightly overlapped the
Gaussian tails (by about 3 1/e2 intensity radii) of the main and repumping barrier
beams. With this geometry, the tail of the repumping barrier beam rapidly pumps
110
any atoms that have been flipped to the F = 1 transmitting state during reflection
back to the F = 2 reflecting state, before they have a chance to reach the main barrier
beam again. Section 4.6.1 examines in detail how the separation affects the barrier’s
performance.
With careful selection of the main-barrier-beam detuning and separation, the one-
way barrier functions as advertised. However, the overlap we employ between the
barrier beams comes at the price of increased scattering. For example, simulations
of the atoms interacting with the barrier that do not take into account the effect
of the repumping barrier beam (state changes or scattering) reveal that an atom
experiences ∼0.7 and ∼8 scattering events during a single transmission and reflection,
respectively. We note that despite the significant detuning between the main barrier
beam and the F = 1 ground state, scattering during transmission is not negligible.
Including heating, state changes and scattering from the repumping barrrier beam as
well as the spatial overlap in the simulations, the number of scattering events during
a single transmission and reflection increases to ∼3 and ∼10, respectively [78, 90].
Though the increased number of scattering events may seem innocuous since many
of them, as described earlier, actually decrease the energy of the atoms, a more
insidious consequence of scattering in general comes from trap losses associated with
light-assisted collisions. The moniker “light-assisted collisions” encompasses several
kinds of excited-state, density-dependent collision processes in cold-atom traps, in-
cluding fine-structure-changing collisions [99], hyperfine changing collisions [100],
111
photo-association [101], and radiative escape [98, 102], all of which result in atom
losses. In particular, we believe the primary culprit responsible for our trap losses is
radiative escape, since this mechanism becomes dominant at trap depths of ∼1 mK.
Here, an atom promoted to an excited state interacts much more strongly with its
neighbors, rapidly accelerating towards them due to its increased polarizability. The
strong interaction stops once the atom has returned to its ground state, but the
kinetic energy gained by each atom during the process is often enough to eject one
or both of them from the trap.
The lifetime for atoms trapped against the barrier speaks to the trap-loss issue.
Figure 4.7(a) shows the population of atoms on both sides of the barrier, initially in
the F = 1 state and loaded to fill the entire trap. At short time scales, the lifetimes
vary from 300 − 500 ms, depending on the temperature of the atoms. Lifetimes
measured after about 200 ms, once the warmest atoms have left the trap, range from
700 − 900 ms, with the data in Figure 4.7(a) yielding a lifetime of about 750 ms.
Though these lifetimes are sufficient for our purposes, they stand in stark contrast
to the 20 s lifetime of atoms in the dipole trap alone (no barrier), illustrating the
magnitude of the losses produced by the excessive scattering of barrier photons during
transmission and reflection.
To support the idea that light-assisted collisions play a role in the observed atom
losses, we included a density-dependent loss mechanism in the simulations that model
the data presented in Figure 4.7(a) [78]. The results of the simulations both with
112
15
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FIG. 16: (Color online) Populations on the left- and right-
hand sides of the one-way barrier, comparing data (points)
to simulations (solid and dashed lines) for a long experiment
showing the barrier lifetime. The trap was initially loaded
nearly symmetrically. The dashed curve shows a simulation
without including light-assisted collisions, which models the
data very poorly. The solid curve shows the same simula-
tions including light-assisted collisions, which matches the
data very closely. For each curve (data and both simulations),
the curves from top to bottom show the total population, the
population on the right side of the barrier, and the population
on the left side of the barrier. Error bars indicate statistical
error from 19 repetitions.
position of each atom one by one, and if they are found
in V1, then they are moved to V2. Once it is known
in which volume an atom resides, a process that swaps
containers need not involve an entropy change, as the two
volumes are of equal size. The demon now has a record
of which volume each atom was found in. In the simplest
case, this memory is a series of N bits each set to 1 or
2. We will assume this memory to be constrained by the
second law of thermodynamics. We will also assume that
the initial state of the memory is known, since writing a
bit over an unknown state is the same as erasing, which,
as described below, requires dumping entropy into the
environment.
If the demon erases the bit after each measurement,
possibly to reuse it, then after each measurement the de-
mon must reduce the phase-space volume of that bit by
a factor of 2. This is because the erasure process must
take two states (representing which volume contained the
particle) and map them into one (the erased state). At-
tempting to avoid this by measuring the state of the bit to
decide how to erase it just transfers the problem to some
other memory that needs to be erased. By the second law
of thermodynamics, this entropy decrease of kB ln 2 must
be accompanied by a matching increase of entropy else-
where, so that the total entropy does not decrease. After
measuring and placing all N atoms, the demon must have
dumped NkB ln 2 of entropy to the outside environment.
If the demon uses N different bits and does not erase
them, then after the cycle is complete the memory is in
one of 2N equally likely states, since each atom was in
either V1 or V2 with equal probability. To an outside ob-
server the atoms are now in a smaller volume, but the
state of the demon’s memory has gone from a known
initial state (zero entropy) to one of 2N possible states,
which is the same entropy increase as if the demon had
erased the bits and dumped that entropy into the envi-
ronment. This also exactly matches the entropy decrease
of the atoms being compressed from two identical vol-
umes into one. The observer cannot know the initial
atomic distribution without having made measurements
of his own, either of the atomic positions or the demon’s
memory. In each case there is an entropy transfer.
Here is a short computer analogy. Assume the atoms
are in a one-dimensional trap, with the position repre-
sented by a number stored in memory. The volume is
proportional to the number of states the number can rep-
resent, and the entropy is proportional to the logarithm
of that, which is proportional to the number of digits, or
bits, in that number. The first bit of the number could
represent whether the atom was located in V1 or V2. The
demon above could be thought of as taking atoms from
V1 and placing them into the exact same place within
V2. In this analogy, that means forcing the first bit of
the number to 1, effectively decreasing the size of the
number by one bit. The number of total digits (entropy)
did not decrease; rather, one was split off and transferred
to the demon’s memory, and no longer represents part of
the atom’s position.
This demon-powered barrier is similar to our one-way
barrier. We can ignore extraneous effects such as photon
recoil (which results in heating), unwanted scattering,
and beam jitter, and still account for entropy. All that
is needed is the irreversible step and the corresponding
measurement record (memory) associated with it. The
“memory” for our one-way barrier is the repumping bar-
rier beam, and it accounts for the entropy even if we ide-
alize it. The ideal repumping barrier beam changes the
state of atoms from F=1 to F=2 and leaves F=2 atoms
alone. That irreversible step can take place because the
transitions available to the F=1 ground state are of a dif-
ferent frequency than those from those available to the
F=2 ground state. When an atom is changed from the
F=1 state to the F=2 state, a repumping-barrier-beam
photon is absorbed and a different photon is emitted. Re-
pump photons cannot change the atom from F=2 back
to F=1, but the lower-frequency emitted photons can.
Completely ignoring random spontaneous emission direc-
tions, we look only at whether the frequency of each pho-
ton is resonant with the F=1 → F ′ transitions or not.
Each photon that is not resonant means that the number
of trapped atoms was increased by one.
Let the trapping volume occupy a fraction r of the to-
tal volume V . It can be shown that the optimum setup
is to have the largest optical depth possible, and as many
untrapped atoms in the trapping region as possible. The
number of untrapped atoms would normally be propor-
tional to the volume ratio r of the trapping region, but
could be lower if many atoms had just been trapped. In
0 2000
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(a) (b)
Figure 4.7. Measured and simulated populations on the left- and right-hand sides
of the barrier up to 2 seconds after initially loading th trap full of atoms. (a)
Data collected showing the lifetime of atoms trapped against the barrier. The error
bars indicate statistical error for 18 repetitions of the experiment. (b) Comparison
of simulations to the data shown in (a). The dashed curves show the res lts of
simulations not including light-assisted collisions, while the solid curves show the
results of simulations including light-assisted collisions. Th simulatio data were
provided by J. J. Thorn.
and without the density-dependent loss mechanism are shown in Figure 4.7(b). The
simulations that model the light-assisted collisions, which had one scali g term that
was fit to the data, are in excellent agreement with t e easured life im da a.
In contrast, simulations that do not model th light assis ed colli ions fit the data
extremely poorly. This suggests that light-assisted collisions are the dominant loss
mechanism for our one-way barrier.
Improving the performance of the barrier almost exclusively depends on increasing
the detuning of the main barrier beam from the transmitting and reflecting states.
One possible scheme for 87Rb [103] makes use of the fine structure and exploits
the F = 1 magnetic sublevels. In particular, it works out that at a wavelength
of 792.5 nm, the optical dipole potential for the mF = +1 state vanishes, while it
113
is positive for the mF = 0,−1 states. Therefore, atoms starting in the mF = +1
sublevel will transmit through the barrier as they experience no potential well or
barrier, while atoms in the mF = −1 sublevel will see a potential barrier blue-detuned
by 2.5 nm from the 795 nm D1 transition. Circularly polarized light resonant with
the F = 1 → F ′ = 1 D2 hyperfine transition optically pumps atoms between the
mF = ±1 states. Another option for increasing the detuning of the main barrier
beam involves implementing the one-way barrier with a different atomic or molecular
species that has a more accommodating level structure. Thorn et al. [78] details a
specific example using 88Sr.
4.5. A Maxwell’s Demon
We devoted a portion of Chapter 3 (Section 3.3) to discussing the one-way barrier
as a physical realization of Maxwell’s demon, and indeed, our barrier is capable of
compressing the phase-space occupied by a sample of atoms. Figure 4.8 shows the
population of atoms on both sides of the barrier after loading the dipole trap off center
for 110 ms, then waiting 200 ms before activating the barrier. The longer load time
fills the trap symmetrically and nearly uniformly with about 9× 104 atoms. Waiting
200 ms for the atoms to settle washes out most of the residual collective motion gained
during the loading process. We lowered the main-barrier-beam power to 18(2) µW
to reduce heating from scattering, since the atoms approach the barrier with less
kinetic energy than in the barrier-demonstration experiments described previously.
114
0 100
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Figure 4.8. Populations on the left- and right-hand sides of the barrier as a function
of time for atoms initially in the F = 1 transmitting state, loaded to fill the entire
trap. The error bars indicate statistical error for 38 repetitions of the experiment.
After activating the barrier, the population on the left-hand side of the trap begins
to decrease as the atoms pass through the one-way barrier and accumulate on the
right-hand side of the trap. Though not all the atoms become trapped, the one-way
barrier is clearly compressing the volume occupied by the atoms in a manner similar
to Maxwell’s demon. The spatial compression results in a 7(2)% decrease in phase-
space volume, which is smaller than might be expected because heating from scattered
barrier photons counteracts a substantial amount of the compression. Optimizing the
barrier parameters for compression would likely improve the reduction in phase-space
volume. Currently, however, the parameters optimize the barrier for transmission
(Section 3.4, 3.5, 3.6).
115
4.6. The Robustness of the Barrier
To characterize the one-way barrier, we evaluated its performance while varying
four key experimental parameters:
1. the separation between the main barrier beam and the repumping barrier beam,
from 8− 74 µm;
2. the initial loading position of the atoms along the dipole-trap axis from 0 −
0.9 mm on both sides of the focus, which represents an effective change in
barrier height;
3. the power of the repumping barrier beam, from 0.002− 8.7 µW; and
4. the detuning of the main barrier beam from the 87Rb F = 2 → F ′ = 3 MOT
trapping transition, blue detuned by +0.75 GHz and +4 GHz from the F = 2
hyperfine ground state.
When assessing the barrier’s performance, we are looking for ideal unidirectional
behavior: namely, all the atoms should reside on the right-hand (reflecting) side of
the barrier after 100 ms of evolution.
In addition to the parameters listed above, we rotated the polarization of the main
barrier beam to match that of the repumping barrier beam, such that both beams
were linearly polarized perpendicular to the dipole-trap axis. This had no obvious
116
effect on the barrier’s performance, implying that main barrier beam’s polarization
is not crucial to the functionality of the barrier.
Throughout the remainder of this chapter, we will frequently refer to the particular
parameter values we utilized during the barrier-demonstration experiments that pro-
duced the data presented in Figure 4.5. Those parameter values produce a nearly
optimum-performing barrier, providing an excellent basis for comparing the effects
of altering these parameters on the barrier’s performance. We will collectively refer
to these parameter values as the “standard values,” corresponding to a 34(1) µm
separation, a 0.65(8) mm loading position, a 0.36(4) µW repumping-barrier-beam
power and a 1.05(5) GHz detuning from the MOT cycling transition.
4.6.1. The Separation
As discussed in Section 4.4, we expect the separation between the main and
repumping barrier beams to play a significant role in the performance of the barrier. In
particular, we reason that too little separation will allow the repumping barrier beam
to pump atoms to the reflecting state before they successfully cross the barrier, while
too much separation will prevent atoms which undergo a state change during reflection
from reaching the repumping barrier beam to correct the state change, causing atoms
to leak back through the barrier. Figure 4.9, which shows the populations as a
function of beam separation on the left- and right-hand sides of the barrier after
100 ms of evolution, gives insight into the validity of this reasoning.
117
(a)
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FIG. 7: (Color online) Populations on the left- and right-hand sides of the one-way barrier after 100 ms as functions of barrier-
beam separation. From left to right, top to bottom, atoms were initially loaded on the left in the F=1 ground state, on the left
in the F=2 ground state, on the right in the F=1 ground state, and on the right in the F=2 ground state. Error bars indicate
statistical error from at least 20 repetitions.
sity. When the repumping barrier beam is too weak to
pump atoms efficiently to the reflecting state, the atoms
continue to transmit through the barrier, resulting in
very little asymmetry, save for whatever side the atoms
happen to be on after 100 ms. However, even at the
weakest intensity used in Fig. 10, the repumping barrier
beam still pumped atoms to the reflecting state and the
barrier acted asymmetrically, although less efficiently. As
the intensity of the repumping barrier beam is increased,
the tails of its beam profile, which extend to the left
(transmitting side) of the main barrier beam, will even-
tually have enough intensity to optically pump atoms on
the left-hand side of the barrier into the reflecting state
before they reach the main barrier beam. In this limit
the barrier becomes reflective on both sides, such that all
atoms will remain to the left of the barrier. Though we do
not reach this limit in our experiment, these two limits to-
gether indicate the existence of an optimum repumping-
barrier-beam intensity that we do observe in Fig. 10.
For the reflecting-side data in Fig. 10, we see the same
decrease in effectiveness as the repumping barrier beam
becomes too weak to pump atoms to the reflecting state.
However, we do not see the same decrease in barrier ef-
ficiency as the repumping-barrier-beam intensity is in-
creased, since a stronger repumping barrier beam just
causes the barrier to reflect better. These behaviors
in the high- and low-intensity limits are evident in the
reflecting-side data shown in Fig. 10, where the barrier
ceases to effectively block atoms as the intensity decreases
but its performance improves and then saturates (pre-
sumably at the point where all atoms reflect) as the in-
tensity increases. At t = 0, the atoms in the dipole trap
have just enough spread that the tails of the distribution
cross the barrier, as can be seen at t = 0 in Fig. 11. This
is a likely explanation as to why the population on the
left-hand side of the barrier is not zero in Fig. 10, even
for the largest repumping-barrier-beam intensities.
We measured population losses for atoms released
on the right-hand side of the barrier for two different
main-barrier-beam detunings (shown in Fig. 12). Fig-
ure 13 shows the results. The near-detuned and far-
detuned data were collected with the main barrier beam
tuned 0.75(5) GHz (using a Fabry-Pe´rot cavity) and
3.97(7) GHz (using the 85Rb F=2 → F ′=2 transition)
blue of the 87Rb MOT trapping transition, respectively.
The near-detuned value was picked to be substantially
(b)
(c) (d)
left-side start, F=1 left-side start, F=2
right-s de tart  F=2right-side start, F=1
Figure 4.9. Populations on the left- and right-hand sides of the barrier as a function
of barri -bea s paration after 100 ms. (a) Atoms starting in the F = 1 transmitting
state on the left-hand side of the trap. (b) Atoms starting in the F = 2 reflecting
state on left-hand s de of the trap. (c) Atoms taring in the F = 1 transmitting
state on the right-hand side of the trap. (d) Atoms starting in the F = 2 reflecting
state on the right-hand sid of the trap. The error b rs indicate statistical error for
at least 20 repetitions of the experiment.
Figures 4.9(a) and 4.9(b) show the effect of the separation on the barrier’s per-
formance for atoms starting on the left-hand side of the trap in the F = 1 and
F = 2 states, respectively. For separations below about 25 µm, the barrier’s ability
to tra smit atoms becomes severely i paired, evidenced by the majority of atoms that
remain on left-hand side of the barrier after 100 ms. This result confirms our reasoning
that at small separations, the Gaussian tail of the repumping barrier beam extends
far enough on the transmitting side of the barrier to optically pump atoms to the
118
reflecting state on either side of the barrier. This undermines the barrier’s asymmetry,
causing it to reflect atoms incident from either direction. Surprisingly though, the
barrier’s performance at large separations does not suffer significantly. The barrier
successfully transmits atoms to the right-hand side of the trap at separations above
30 µm, however, the effectiveness of the barrier does decline slightly beyond about
50 µm. We attribute the decline to the reasoning that at smaller separations, most
atoms will pass back through the repumping barrier beam after reflection, ensuring
that any atoms pumped to the transmitting state while interacting with main barrier
beam return to the reflecting state. At larger separations, however, some atoms may
not reach the repumping barrier beam to correct for any state changes that occurred
during reflection. This enables them to pass back through the barrier, reducing the
population on the right-hand side of the trap. This effect is not as pronounced as we
had anticipated, though, indicating that while overlapping the beams is necessary to
optimize reflection from the barrier, it is not critical to barrier operation.
Section 4.4 explored the main drawback of employing some spatial overlap between
the main and repumping barrier beams, highlighting the concomitant trap losses.
Interestingly, this phenomenon is manifest in the data presented in Figures 4.9(a)
and 4.9(b). Examining the total population data for both plots reveals a marked
decrease in the total normalized population (the population at t = 100 ms compared
to the population at t = 0) for separations that have non-negligible overlap (about
3 1/e2 radii, or 40 µm apart). We believe the increased losses reflect the additional
119
scattering of photons due to the stronger repumping-barrier-beam component in the
region of the main barrier beam. This produces more state changes, as the beams
are more likely to optically pump the atoms between the two hyperfine ground-states
during transmission. The stronger repumping-barrier-beam component also increases
heating from scattering, since the atoms are more likely to change state in the middle
of the barrier beam (as opposed to the side), where the potential energy increase
associated with switching to the F = 2 reflecting state is substantial.
Figures 4.9(c) and 4.9(d) show how the separation impacts the reflectivity of the
barrier for atoms starting on the right-hand side of the trap in the F = 1 and F = 2
states, respectively. Unlike the transmitting ability of the barrier, its reflectivity is
quite robust to the beam separation, showing no dramatic changes throughout the
range of separations. The effectiveness of the barrier decreases mildly above about
50 µm, exhibiting the same phenomena observed for larger separations (above 50 µm)
in the left-hand-side results discussed earlier. These data suggest that as long as the
repumping barrier beam is present to the right of the main barrier beam, the barrier’s
ability to reflect atoms remains largely intact.
4.6.2. The Loading Position
We also examined how loading the atoms at different positions along the dipole-
trap axis affects the performance of the barrier. Altering the loading position of the
atoms relative to the trap center changes the kinetic energy of the atoms, which we use
as substitute for varying the height of the potential barrier. Though we can adjust
120
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FIG. 8: (Color online) Populations on the left- and right-
hand sides of the one-way barrier after 100 ms as functions
of initial loading position. The initial loading position is the
position of the zero of the MOT magnetic fields relative to
the focus of the dipole trap, in millimeters. Our canonical
starting locations were about 0.65(8) mm away from the focus
of the dipole trap and are marked by the two vertical gray
regions. Vertical error bars indicate statistical error from 38
repetitions, and horizontal error bars indicate uncertainty in
measuring the MOT center.
0 20 40 60 80 100
0
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1.0
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right
left
(a)
(a)
(b)
(b)
(c)
(c)
(d)
(d)
(e)
(e)
FIG. 9: (Color online) Some sample time-series that formed
the data in Fig. 8, showing populations on the right- and
left-hand sides of the barrier as functions of time. Shown
are curves for initial loading positions of (a) 0.89(8) mm,
(b) 0.43(8) mm, (c) 0.14(8) mm, (d) −0.51(8) mm, and (e)
−0.90(8) mm from the barrier center. Error bars indicate
statistical error from 38 repetitions.
closer to the F=2 → F ′ resonances than our canoni-
cal value, but not so close as to increase scattering of
the barrier-beam light enough to prevent barrier oper-
ation. The far-detuned value was conveniently close to
halfway between the resonances for F=1 (transmitting)
and F=2 (reflecting) atoms, and is actually a little closer
to the F=1 resonances. This allowed us to compare
a more symmetric detuning to our canonical case and
test how damaging state-changing scattering events are
to the barrier operation. For both of these data sets,
the intensity of the main barrier beam was adjusted so
that the height of the reflecting barrier was the same
as for our canonical data (with the barrier tuned to the
85Rb MOT transition), which is also shown in Fig. 13.
The near-detuned data are nearly indistinguishable from
our canonical reflecting-side data. The far-detuned data
show a much shorter lifetime, but no extra leakage to the
reflecting side of the barrier. This indicates the following:
1. Heating from scattering barrier-beam light alone is
not much of a problem. If it were, then the near-
detuned data, which should have ∼2 times as much
scattering as our canonical data because it is closer
to resonance, should show much more loss.
2. State-changing from scattering barrier-beam light
is an issue. We believe we can explain this as fol-
lows. In both our canonical data and the near-
detuned data, the barrier was much more likely
to pump atoms to the transmitting state, which
decreases the potential energy of the atoms, thus
helping to cool them. The repumping barrier beam
pumps to the reflecting state, but since that oc-
curs away from the barrier beam, heating due to
the potential-energy increase is small. In the far-
detuned data, the main barrier beam can pump
atoms to either state. Atoms in the transmitting
state that are pumped to the reflecting state are
likely to be ejected from the barrier at high speed.
Atoms in the reflecting state that are pumped to
the transmitting state are more likely to be mov-
ing slowly, because they were being reflected, which
makes them likely to scatter again. Thus, atoms
leaving the beam after a state change are more
likely to have been heated than cooled. This in-
creased heating decreases the trap lifetime substan-
tially. Appendix B discusses scattering in more
depth.
We also briefly tried having both the main barrier
beam and the repumping barrier beam polarized parallel
to the longitudinal axis of the dipole-trap beam. We saw
no significant change, suggesting that the barrier opera-
tion is insensitive to polarization.
V. SIMULATIONS
We simulated the barrier operation using a simple
model where atoms were assumed to be noninteracting
point particles with well-defined positions and momenta.
These atoms move in conservative potentials formed by
the dipole-trap beam and the main barrier beam. At
every point in time the atoms were assumed to be in ei-
ther the F=1 (transmitting) or F=2 (reflecting) ground
state. This is because coherences between these states os-
cillate at much faster time scales (subnanosecond) than
the center-of-mass motion (microseconds to milliseconds)
Figure 4.10. Populations on the left- and right-hand sides of the barrier as a function
of loading position after 100 ms for atoms started in the F = 1 state. Negative
(positive) loading positions indicate atoms starting on the left-hand (right-hand) side
of the trap. The vertical, gray bars delineate the standard value for the starting
position. The vertical err r bars indicate statistical error for 38 repetitions of the
experiment, and the h rizontal error bars r flect uncertainty in measuring the
center of the MOT to determine the displacement.
the ratio of atomic kinetic energy to barrier height by changing either the loading
position or the power of the main barrier beam, each change has a different effect on
the number of scattering events expected as the atoms traverse the barrier. Appendix
B in Thorn et al. [78] examines this topic in detail.
Figure 4.10 presents the populations on the left- and right-hand sides of the barrier
(for atoms starting in the F = 1 state) as a function of loading position after 100 ms
of evolution. The initial loading position is given by the difference between he
center of the atomic cloud after the half-period delay (Section 4.3) and the focus
of the dipole trap (position zero), measured in millimeters. This is defined such
that negative loading positions start atoms on the left-hand side of the barrier and
121
positive ones start atoms on the right-hand side. The vertical, gray bars indicate
the standard value for the starting position, which had an initial displacement of
about ±0.65(8) mm (averaged between the left- and right- start values). We see
that the populations on either side of the barrier remain constant regardless of the
loading position, indicating that the barrier functions equally well for a wide range of
atomic velocities. Figure 4.11 shows a sample of the type of data aggregated to create
Figure 4.10, which monitors the populations on both sides of the barrier as function
of time for various initial loading positions. The atoms in data sets (a), (b), and (c)
start on the right-hand side of the barrier and proceed to remain there, while the
atoms in data sets (d) and (e) start on the left-hand side, then successfully transmit
through the barrier where they remain trapped. Little distinguishes the five data
sets after about 30 ms, reinforcing the conclusion that the barrier operates effectively
regardless of the atomic kinetic energy.
4.6.3. The Repumping-Barrier-Beam Power
The repumping barrier beam plays a crucial role in the functioning of the one-way
barrier in that it is responsible for the desired unidirectional behavior. Without it, the
barrier would exclusively transmit or reflect atoms depending on their initial state,
barring any optical pumping due to the main barrier beam. We varied the power
of the repumping barrier beam by more than three orders of magnitude to assess its
effect on the performance of the barrier. Figure 4.12 presents our results, showing the
populations on both sides of the barrier after 100 ms as a function of repumping-
122
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FIG. 8: (Color online) Populations on the left- and right-
hand sides of the one-way barrier after 100 ms as functions
of initial loading position. The initial loading position is the
position of the zero of the MOT magnetic fields relative to
the focus of the dipole trap, in millimeters. Our canonical
starting locations were about 0.65(8) mm away from the focus
of the dipole trap and are marked by the two vertical gray
regions. Vertical error bars indicate statistical error from 38
repetitions, and horizontal error bars indicate uncertainty in
measuring the MOT center.
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1.0
time (ms)
p
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right
left
(a)
(a)
(b)
(b)
(c)
(c)
(d)
(d)
(e)
(e)
FIG. 9: (Color online) Some sample time-series that formed
the data in Fig. 8, showing populations on the right- and
left-hand sides of the barrier as functions of time. Shown
are curves for initial loading positions of (a) 0.89(8) mm,
(b) 0.43(8) mm, (c) 0.14(8) mm, (d) −0.51(8) mm, and (e)
−0.90(8) mm from the barrier center. Error bars indicate
statistical error from 38 repetitions.
closer to the F=2 → F ′ resonances than our canoni-
cal value, but not so close as to increase scattering of
the barrier-beam light enough to prevent barrier oper-
ation. The far-detuned value was conveniently close to
halfway between the resonances for F=1 (transmitting)
and F=2 (reflecting) atoms, and is actually a little closer
to the F=1 resonances. This allowed us to compare
a more symmetric detuning to our canonical case and
test how damaging state-changing scattering events are
to the barrier operation. For both of these data sets,
the intensity of the main barrier beam was adjusted so
that the height of the reflecting barrier was the same
as for our canonical data (with the barrier tuned to the
85Rb MOT transition), which is also shown in Fig. 13.
The near-detuned data are nearly indistinguishable from
our canonical reflecting-side data. The far-detuned data
show a much shorter lifetime, but no extra leakage to the
reflecting side of the barrier. This indicates the following:
1. Heating from scattering barrier-beam light alone is
not much of a problem. If it were, then the near-
detuned data, which should have ∼2 times as much
scattering as our canonical data because it is closer
to resonance, should show much more loss.
2. State-changing from scattering barrier-beam light
is an issue. We believe we can explain this as fol-
lows. In both our canonical data and the near-
detuned data, the barrier was much more likely
to pump atoms to the transmitting state, which
decreases the potential energy of the atoms, thus
helping to cool them. The repumping barrier beam
pumps to the reflecting state, but since that oc-
curs away from the barrier beam, heating due to
the potential-energy increase is small. In the far-
detuned data, the main barrier beam can pump
atoms to either state. Atoms in the transmitting
state that are pumped to the reflecting state are
likely to be ejected from the barrier at high speed.
Atoms in the reflecting state that are pumped to
the transmitting state are more likely to be mov-
ing slowly, because they were being reflected, which
makes them likely to scatter again. Thus, atoms
leaving the beam after a state change are more
likely to have been heated than cooled. This in-
creased heating decreases the trap lifetime substan-
tially. Appendix B discusses scattering in more
depth.
We also briefly tried having both the main barrier
beam and the repumping barrier beam polarized parallel
to the longitudinal axis of the dipole-trap beam. We saw
no significant change, suggesting that the barrier opera-
tion is insensitive to polarization.
V. SIMULATIONS
We simulated the barrier operation using a simple
model where atoms were assumed to be noninteracting
point particles with well-defined positions and momenta.
These atoms move in conservative potentials formed by
the dipole-trap beam and the main barrier beam. At
every point in time the atoms were assumed to be in ei-
ther the F=1 (transmitting) or F=2 (reflecting) ground
state. This is because coherences between these states os-
cillate at much faster time scales (subnanosecond) than
the center-of-mass motion (microseconds to milliseconds)
Figure 4.11. Populations on the left- and right-hand sides of the barrier as a function
of time for several different loading positions for atoms started in the F = 1 state.
The initial displacement for the five different data runs are a 0.89(8) mm, (b)
0.43(8) mm, c) 0.14( , (d −0.51(8) m and (e) −0.90(8) mm. The error bars
indicate statistical error for 38 repetitions of the experiment.
barrier-beam power for atoms starting on the left- [Fig. 4.12(a)] and right-hand
[Fig. 4.12(b)] sides of the trap. For comparison, the vertical lines indicate the standard
repumping-barrier-beam power, while the horizontal bars show the populations after
100 ms for data collected with no barrier. In this case, the collective motion of
the atoms produces the unequal populations visible on each side of the barrier [see
Figure 4.13(a) and 4.13(b)]. Overall, the functionality of the one-way barrier remains
intact over the wide range of repumping-barrier-beam intensities we studied, though
the minimum and maximum intensity extremes substantially impact its efficiency.
Figure 4.12(a) reveals that the barrier retains at least some ability to transmit and
subsequently reflect atoms over the broad range of repumping-barrier-beam powers,
123
main barrier
beam
absorption
imaging beam
CCD camera
dipole-trap
beam repumping
barrier beam
main barrier
beam
absorption
imaging beam
CCD camera
dipole-trap
beam repumping
barrier beam
11
repump beam power (mW)
p
op
u
la
ti
on
 (
n
or
m
al
iz
ed
)
Transmitting side
0.001 0.01 0.1 1 10
0
0.2
0.4
0.6
0.8
1.0
left
right
total
no barrier, left
no barrier, right
Reflecting side
0.001 0.01 0.1 1 10
0
0.2
0.4
0.6
0.8
1.0
left
right
total
no barrier, left
no barrier, right
FIG. 10: (Color online) Populations on the left- and right-hand sides of the one-way barrier after 100 ms as functions of
repumping-barrier-beam power. The left panel shows results where the atoms were initially on the left-hand (transmitting)
side of the barrier, and the right panel shows results where the atoms were initially on the right-hand (reflecting) side. The
vertical lines in the plots show our usual repumping-barrier-beam power of 0.36 µW. The two horizontal bars show the ending
populations from data taken with no barriers [the one shown in column (a) of Fig. 4 and a similar data set where atoms
were initially on the other side of the barrier]. The no-barrier cases show unequal left- and right-hand populations due to the
oscillations of the atoms. Error bars indicate statistical error from at least 38 repetitions.
time (ms)
p
op
u
la
ti
on
 (
n
or
m
al
iz
ed
)
Transmitting side
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1.0
left
right
total
Reflecting side
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1.0
left
right
total
Transmitting side (no barrier)
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1.0
left
right
total
Reflecting side (no barrier)
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1.0
left
right
total
FIG. 11: (Color online) Populations on the left- and right-hand sides of the one-way barrier for a few different repumping-
barrier-beam powers as functions of time. The top two panels show data collected without barrier beams. The bottom two
panels are generated from the same data used in Fig. 10. The data with the dotted line and squares correspond to the minimum
beam power (about 2 nW) shown in Fig. 10. The data with the dashed line and diamonds correspond to approximately the
same power used to collect our canonical data. The data with the solid line and triangles correspond to the maximum beam
power (about 9 µW) shown in Fig. 10. The top curve in each panel shows the total population, while the other solid symbols
show the right-hand side population and the open symbols show the left-hand side population.
(a) (b)
left- ide start right-side start
Figure 4.12. Populations on the left- and right-hand sides of the barrier as a function
of repumping-barrier-beam power afte 100 ms. (a) Atoms sta ti g in t e F = 1
transmitting state on the left-hand side of the trap. (b) Atoms starting in F = 1
transmitting state on the right-hand side of the trap. The vertical line marks the
0.36 µW standard value for the repumping-barrier-beam power. The horizontal bars
show the popula ions aft r 100 ms for data collected with no barrier. The error bars
indicate statistical error for at least 38 repetitions of the experiment.
evidenced by a majority of atoms collecting on the right-hand side of the barrier
regardless of the power. A weak optimum also exists in the left-hand-side data,
indicating that the barrier’s unidirectional behavior starts to break down at very low
and very high intensities. We expect the barrier to lose its asymmetry at very low
repumping-barrier-beam intensities, since the repumping barrier beam becomes too
weak to efficiently pump atoms to the reflecting state after they transmit through the
barrier, allowing them to pass back through. In this limit, the collective motion of
the atoms determines the populations on each side of the barrier, eventually reaching
a st ady state of 50%. Though we do not reach his limit in our exp riment, we s ill
observe that the barrier’s unidirectional performance diminishes at low intensities.
Despite this reduction in efficiency, a small amount of asymmetry persists in the
124
populations in Figure 4.12(a) at the minimum power, demonstrating that the barrier
remains weakly functional even at extremely small repumping-barrier-beam inten-
sities. At very high intensities, the Gaussian tails of the repumping barrier beam,
which extend to the left side of the main barrier beam, contain a significant amount
of power. This enables the repumping barrier beam to optically pump atoms to the
reflecting state prior to encountering the main barrier beam, such that the atoms
reflect off the barrier and remain trapped on the left-hand side. Though the data
presented in Figure 4.12(a) do not approach this limit as some asymmetry remains
visible, we observe the expected downward trend in the right-hand-side populations
at higher powers.
The data presented in Figure 4.12(b) show how the intensity of the repumping
barrier beam affects the reflectivity of the barrier. The population on the right-hand
side of the barrier exhibits a notable decrease at smaller intensities, which is another
manifestation of the low-intensity behavior described previously for the left-hand-side
results. In this case, the repumping barrier beam lacks the intensity to successfully
pump atoms to the reflecting state, such that the barrier ceases to reflect atoms
effectively. In contrast to the left-hand-side results, however, the barrier’s reflectivity
improves and then saturates at higher repumping-barrier-beam intensities, suffering
no decrease in efficiency. The small number of atoms observed on the left-hand side
of the trap even at the highest intensities result from the atomic cloud extending to
the left of the trap center when the barrier is turned on. The lack of dependence of
125
the barrier’s performance on the increasing intensity of the repumping barrier beam
reflects the fact that any intensity increase—beyond that necessary to optically pump
all the atoms to the reflecting state—has no impact on the barrier’s reflectivity. In
fact, the repumping barrier beam itself becomes a formidable, low scattering barrier
at high enough intensities, as it is blue detuned by 6.8 GHz from the F = 2 reflecting
state of the trapped atoms.
To highlight the influence that the repumping-barrier-beam intensity has on the
atomic dynamics, Figure 4.13 shows populations on both sides of the barrier as a
function of time for the lowest and highest intensities starting on the left- [Fig.4.13(c)]
and right-hand [Fig.4.13(d)] sides of the barrier. For comparison, the time series for
the standard value of the repumping-barrier-beam intensity and the data collected
with no barrier [Figs. 4.13(a) and 4.13(b)] are included as well. In Figure 4.13(c),
we see that the minimum- and maximum-intensity data exhibit some oscillation
of the population back and forth across the barrier, though the two curves never
cross after the initial transmission through the barrier at t ∼ 13 ms (unlike the no-
barrier data, which crosses several times), demonstrating that the barrier retains some
asymmetry even at the highest and lowest intensities. For the atoms starting on the
right-hand side of the trap [Fig. 4.13(d)], only the minimum-intensity data display
population oscillations, almost crossing at t ∼ 19 ms, illustrating how the intensity
of the repumping barrier beam compromises the barrier’s performance at very small
intensities while preserving its reflectivity at high intensities.
126
11
repump beam power (mW)
p
op
u
la
ti
on
 (
n
or
m
al
iz
ed
)
Transmitting side
0.001 0.01 0.1 1 10
0
0.2
0.4
0.6
0.8
1.0
left
right
total
no barrier, left
no barrier, right
Reflecting side
0.001 0.01 0.1 1 10
0
0.2
0.4
0.6
0.8
1.0
left
right
total
no barrier, left
no barrier, right
FIG. 10: (Color online) Populations on the left- and right-hand sides of the one-way barrier after 100 ms as functions of
repumping-barrier-beam power. The left panel shows results where the atoms were initially on the left-hand (transmitting)
side of the barrier, and the right panel shows results where the atoms were initially on the right-hand (reflecting) side. The
vertical lines in the plots show our usual repumping-barrier-beam power of 0.36 µW. The two horizontal bars show the ending
populations from data taken with no barriers [the one shown in column (a) of Fig. 4 and a similar data set where atoms
were initially on the other side of the barrier]. The no-barrier cases show unequal left- and right-hand populations due to the
oscillations of the atoms. Error bars indicate statistical error from at least 38 repetitions.
time (ms)
p
op
u
la
ti
on
 (
n
or
m
al
iz
ed
)
Transmitting side
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1.0
left
right
total
Reflecting side
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1.0
left
right
total
Transmitting side (no barrier)
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1.0
left
right
total
Reflecting side (no barrier)
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1.0
left
right
total
FIG. 11: (Color online) Populations on the left- and right-hand sides of the one-way barrier for a few different repumping-
barrier-beam powers as functions of time. The top two panels show data collected without barrier beams. The bottom two
panels are generated from the same data used in Fig. 10. The data with the dotted line and squares correspond to the minimum
beam power (about 2 nW) shown in Fig. 10. The data with the dashed line and diamonds correspond to approximately the
same power used to collect our canonical data. The data with the solid line and triangles correspond to the maximum beam
power (about 9 µW) shown in Fig. 10. The top curve in each panel shows the total population, while the other solid symbols
show the right-hand side population and the open symbols show the left-hand side population.
(b)
(c) (d)
left-side start, no barrier right-s de start, no barrier
right-side start, with barrierleft-side start, with barrier
(a)
Figure 4.13. Populations on the left- and right-hand sides of the barrier as a function
of time for: (a) Atoms starting in the F = 1 tate o the left-hand side of the trap
without the barrier. (b) Atoms starting in the F = 1 state on the right-hand side
of the trap without the barrier. (c) Atoms starting in the F = 1 state on the left-
hand side of the trap for the minimum (about 2 nW, dotted lines), maximum (about
9 µW, solid lines), and standard (0.36 µW, dashed lines) repumping-barrier-beam
powers. (d) Atoms starting in the F = 1 state on the right-hand side of the trap
for the minimum (dotted lines), maximum (solid lines), and standard (dashed lines)
repumping-barrier-beam powers.
4.6.4. The Main-Barrier-Beam Detuning
Selecting an appropriate detuning for the main barrier beam that optimizes barrier
performance while minimizing unnecessary scattering events was the main technical
challenge associated with implementing the one-way barrier. In particular, choosing a
detuning that minimized atom loss during transmission (Section 4.4) resulted in the
standard 1.05(5) GHz detuning we employed for the barrier demonstration exper-
127
iments. Here we investigate how different choices of main-barrier-beam detuning
affect losses for atoms starting on the right-hand (reflecting) side of the barrier.
We present data for three different, blue-detuned main-barrier-beam frequencies,
each measured relative to the 87Rb F = 2 → F ′ = 3 MOT trapping transition: (1)
The standard value of 1.05(5) GHz we utilized for the demonstration experiments,
generated by locking the main barrier beam to the 85Rb F = 3→ F ′ = 3, 4 crossover
transition; (2) A near-detuned value of 0.75(5) GHz, obtained by coupling a fraction
of the main-barrier-beam and the MOT trapping beam into a 1.5 GHz Fabry-Perot
cavity, then tuning the main-barrier-beam frequency half way between the MOT-
trapping-beam transmission peaks; and (3) A far-detuned value of 3.97(7) GHz,
produced by stabilizing the main barrier beam to the 85Rb F = 2→ F ′ = 2 transition.
The values of these detunings relative to the MOT trapping transition are illustrated
in Figure 4.14. For each detuning, we adjust the power of the main barrier beam
to ensure that the height of the potential barrier presented to the reflecting atoms
remains the same (Section 1.6). Changing the power and detuning of the main barrier
beam impacts the number of scattering events we expect for an atom reflecting from
the barrier. In particular, we selected the near-detuned value because it is much
closer to the F = 2 → F ′ = 3 transition than our standard value, but not so much
as to substantially increase the expected number of scattering events, which should
go up by about a factor of 2. The far-detuned value conveniently lies about halfway
between the F = 1 and F = 2 resonances, and has been employed for atoms starting
128
Rb
87
Rb85
0.75 GHz
3.97 GHz
1.05 GHz
near-detuned
standard-detuned
far-detuned
F=2       F!
F=2       F!
F=3       F!
F=1       F!
Rb85
Rb
87
12
-1 0 2 4 6
detuning (GHz)
87Rb
Fo=o1! oFo! '
87Rb
Fo=o2! oFo!'  
85Rb
 Fo=o2! oFo!'
85Rb
  Fo=o3! oFo!'
near-detuned
0.75 GHz
canonical
1.05 GHz
far-detuned
3.97 GHz
FIG. 12: (Color online) A schematic of the rubidium emis-
sion spectrum around the D2 line, showing the detunings we
tested for the main barrier laser. The horizontal axis mea-
sures detuning from the 87Rb F=2 → F ′=3 MOT trapping
transition. Both 87Rb and 85Rb resonances are shown. Our
canonical detuning coincides with the 85Rb F=3 → F ′=3, 4
crossover transition, and the far-detuned value coincides with
the 85Rb F=2 → F ′=2 transition. For the near-detuned
value, we monitored the detuning with a Fabry-Pe´rot cav-
ity. Each detuning from the 87Rb MOT trapping transition
is shown with a solid arrow. This approximates the detuning
seen by atoms in the F=2 (reflecting) state. A dotted arrow
shows the detuning from the 87Rb MOT repumping transi-
tion, which approximates the detuning seen by atoms in the
F=1 (transmitting) state.
0 100 200 300 400 500
0
0.2
0.4
0.6
0.8
1.0
time (ms)
p
op
u
la
ti
on
 (
n
or
m
al
iz
ed
)
left
“far” right
“near” right
canonical right
FIG. 13: (Color online) Populations on the left- and right-
hand sides of the one-way barrier, comparing barrier per-
formances when the main barrier laser operates at differ-
ent frequencies. For the canonical, near-detuned, and far-
detuned data, the main-barrier detunings were 1.05(5) GHz,
0.75(5) GHz, and 3.97(7) GHz blue of the 87Rb MOT transi-
tion, respectively. See Fig. 12 for details. The near-detuned
and canonical data are very similar, while the far-detuned
data show much more atom loss. Error bars indicate statisti-
cal error from at least 28 repetitions.
of the atoms, and so can be time averaged, effectively al-
lowing each atom to be in a classical mixture of the two
ground states.
The potential the atoms move in is a sum of potentials
from the dipole-trap beam and the main barrier beam.
We assume the strengths of the potentials to be propor-
tional to the local beam intensities. We use far-detuned
approximations for computing the potentials, and we also
use the rotating-wave and two-level-atom approximations
for the barrier beams. The repumping barrier beam
pumps atoms out of the F=1 ground state very quickly,
and is too weak and too far detuned to produce a strong
potential for atoms in the F=2 ground state, so we ignore
its potential. After each time step of the integration, we
compute a local scattering rate for each atom given the
beam intensities at the atom’s position and the current
atomic state. The dipole-trap beam is very far detuned
and has a scattering rate on the order of 3 s−1, which we
ignore—in our simulation only the barrier beams scatter
off the atoms. We then randomly decide whether each
atom scatters a photon in this time step, with a prob-
ability equal to the scattering rate times the time step.
A scattering event is modeled by a randomly directed
(with a dipole-emission distribution) single-photon recoil
kick applied to the momentum, and a randomly chosen
atomic state change based on the probabilities computed
in Appendix A.
We found that the simulations were somewhat sensitive
to initial conditions (compare Fig. 14 with Fig. 15). We
achieved very good agreement between simulation and
experiment with the following initial conditions: Atoms
were initially placed in an oblong Gaussian ellipsoid,
placed to match the initial conditions of the atoms in
the experiment we were modeling. The long axis lies
along the dipole-trap axis, with a length comparable to
that measured in our experiments (we used a standard
deviation of 400 µm). The two short-axis widths were
chosen so that most of the atoms started out trapped
in the dipole trap, with some small variations to help
match the simulations to the data. The momenta for each
atom were initialized to random values with a ∼100 µK
Maxwell-Boltzmann distribution. We also simulated the
nonzero loading time. For each atom we picked a uni-
formly distributed random start time that was less than
the loading time. Each atom is frozen until its chosen
start time, at which point its position and momentum
begin to change according to the rules described above.
This emulates the actual loading procedure, where atoms
enter the dipole-trap beam and become trapped through-
out the loading time. Atoms just entering the trapping
region do so with random momenta because atoms in a
MOT scatter often. Once trapped in the dipole trap they
become dark to the MOT beams and begin evolving ac-
cording to the dipole-trap potential. Thus, atoms that
have spent time in the trap have a preferred direction and
position different from atoms that have just been loaded,
as they have begun moving toward the dipole-trap focus.
This gives a slight position-momentum correlation that
stand rd-detuned
Figure 4.14. A schematic showing the 87Rb D2 emission spectrum and the three
detunings used to test the reflectivity of the barrier. The horizontal axis displays the
detunings relative to the 87Rb F = 2→ F ′ = 3 MOT trapping transition. The solid
lines indicate the blue detunings of the barrier for atoms in the F = 2 reflecting s at ,
while the dashed lines show the approxima e red detunings of the barrier for atoms
in the F = 1 transmitting state. Figure created by J. J. Thorn.
on the left-hand side of the barrie previously, producing sig ificant trap losses during
transmission (Section 4.4).
Figure 4.15 presents the results, showing the populations on both sides of the
barrier for up to 500 ms as a function of time. The populations on the left-hand
side of the trap are nearly identical for all three detunings, indicating that the
barrier successfully prevents transmission of atoms regardless of its detuning. The
populations on the right-hand side of the trap remain similar for the near-detuned
and standard values; however, we observe a dramatic reduction in population for the
129
Helmholtz
Coils
Anti-Helmholtz
Hellma
Cell
Coils
12
-1 0 2 4 6
detuning (GHz)
87Rb
Fo=o1! oFo! '
87Rb
Fo=o2! oFo!'  
85Rb
 Fo=o2! oFo!'
85Rb
  Fo=o3! oFo!'
near-detuned
0.75 GHz
canonical
1.05 GHz
far-detuned
3.97 GHz
FIG. 12: (Color online) A schematic of the rubidium emis-
sion spectrum around the D2 line, showing the detunings we
tested for the main barrier laser. The horizontal axis mea-
sures detuning from the 87Rb F=2 → F ′=3 MOT trapping
transition. Both 87Rb and 85Rb resonances are shown. Our
canonical detuning coincides with the 85Rb F=3 → F ′=3, 4
crossover transition, and the far-detuned value coincides with
the 85Rb F=2 → F ′=2 transition. For the near-detuned
value, we monitored the detuning with a Fabry-Pe´rot cav-
ity. Each detuning from the 87Rb MOT trapping transition
is shown with a solid arrow. This approximates the detuning
seen by atoms in the F=2 (reflecting) state. A dotted arrow
shows the detuning from the 87Rb MOT repumping transi-
tion, which approximates the detuning seen by atoms in the
F=1 (transmitting) state.
0 100 200 300 400 500
0
0.2
0.4
0.6
0.8
1.0
time (ms)
p
op
u
la
ti
on
 (
n
or
m
al
iz
ed
)
left
“far” right
“near” right
canonical right
FIG. 13: (Color online) Populations on the left- and right-
hand sides of the one-way barrier, comparing barrier per-
formances when the main barrier laser operates at differ-
ent frequencies. For the canonical, near-detuned, and far-
detuned data, the main-barrier detunings were 1.05(5) GHz,
0.75(5) GHz, and 3.97(7) GHz blue of the 87Rb MOT transi-
tion, respectively. See Fig. 12 for details. The near-detuned
and canonical data are very similar, while the far-detuned
data show much more atom loss. Error bars indicate statisti-
cal error from at least 28 repetitions.
of the atoms, and so can be time averaged, effectively al-
lowing each atom to be in a classical mixture of the two
ground states.
The potential the atoms move in is a sum of potentials
from the dipole-trap beam and the main barrier beam.
We assume the strengths of the potentials to be propor-
tional to the local beam intensities. We use far-detuned
approximations for computing the potentials, and we also
use the rotating-wave and two-level-atom approximations
for the barrier beams. The repumping barrier beam
pumps atoms out of the F=1 ground state very quickly,
and is too weak and too far detuned to produce a strong
potential for atoms in the F=2 ground state, so we ignore
its potential. After each time step of the integration, we
compute a local scattering rate for each atom given the
beam intensities at the atom’s position and the current
atomic state. The dipole-trap beam is very far detuned
and has a scattering rate on the order of 3 s−1, which we
ignore—in our simulation only the barrier beams scatter
off the atoms. We then randomly decide whether each
atom scatters a photon in this time step, with a prob-
ability equal to the scattering rate times the time step.
A scattering event is modeled by a randomly directed
(with a dipole-emission distribution) single-photon recoil
kick applied to the momentum, and a randomly chosen
atomic state change based on the probabilities computed
in Appendix A.
We found that the simulations were somewhat sensitive
to initial conditions (compare Fig. 14 with Fig. 15). We
achieved very good agreement between simulation and
experiment with the following initial conditions: Atoms
were initially placed in an oblong Gaussian ellipsoid,
placed to match the initial conditions of the atoms in
the experiment we were modeling. The long axis lies
along the dipole-trap axis, with a length comparable to
that measured in our experiments (we used a standard
deviation of 400 µm). The two short-axis widths were
chosen so that most of the atoms started out trapped
in the dipole trap, with some small variations to help
match the simulations to the data. The momenta for each
atom were initialized to random values with a ∼100 µK
Maxwell-Boltzmann distribution. We also simulated the
nonzero loading time. For each atom we picked a uni-
formly distributed random start time that was less than
the loading time. Each atom is frozen until its chosen
start time, at which point its position and momentum
begin to change according to the rules described above.
This emulates the actual loading procedure, where atoms
enter the dipole-trap beam and become trapped through-
out the loading time. Atoms just entering the trapping
region do so with random momenta because atoms in a
MOT scatter often. Once trapped in the dipole trap they
become dark to the MOT beams and begin evolving ac-
cording to the dipole-trap potential. Thus, atoms that
have spent time in the trap have a preferred direction and
position different from atoms that have just been loaded,
as they have begun moving toward the dipole-trap focus.
This gives a slight position-momentum correlation that
standard-detuned, right
near-detuned, right
far-detuned,
right
Figure 4.15. Populations on the right- and left-hand sides of the trap as a function
of time for three different main-barrier-beam detunings. The atoms initially started
in the F = 1 transmitting state on the right-hand side of the trap. The three main-
barrier-beam- t nings were 0.75(5) GHz, 1.05(5) GHz, and 3.97(7) GHz blue of
the 87Rb MOT trapping transition for the near-detuned, standard-detuned, and far-
detuned data, respectively. The error bars indicate statistical error for at least 28
repetitions of the experiment.
far-detuned value. We can explain these behaviors in the context of the state changes
an atom can undergo when reflecting from the barrier. In particular, an atom that
flips from the F = 1 transmitting state to the F = 2 reflecting state in the presence
of the main barrier beam under goes a devastating state change, as it experiences a
substantial increase in potential energy, and will likely be ejected from the barrier at
high speed. On the other hand, and atom that changes from the F = 2 reflecting
state to the F = 1 transmitting state undergoes a relatively harmless state change,
as it experiences a reduction in potential energy, which cools the atom.
130
An atom reflecting from the near-detuned and standard-detuned barriers will
have a very similar experience, in that for both detunings, the main barrier beam
easily pumps reflecting atoms to the F = 1 transmitting state due to its proximity
to the F = 2 → F ′ = 3 resonance—a relatively harmless state change. These
detunings, however, do not effectively pump atoms back to the F = 2 reflecting state,
which minimizes these devastating state changes. An atom that has been pumped
to the transmitting state during a reflection will nearly exit the main barrier beam
before encountering the repumping barrier beam to correct the state change. At this
position, near the edge of the main barrier beam, the potential energy increase from
flipping back to the reflecting state is minimal. The data in Figure 4.15 suggest that
heating solely from scattering barrier-beam photons (that produce relatively harmless
state changes) is not a primary source of atom loss, since the near-detuned data, which
should suffer about twice as many scattering events, exhibit only slightly more loss.
The situation changes, however, for the far-detuned barrier, for which atoms in
either state scatter similar amounts of light. Under these circumstances, an atom
reflecting from the barrier may initially undergo a relatively harmless state change
to the F = 1 transmitting state, but is much more likely to experience a subsequent,
devastating state change to the F = 2 reflecting state. This devastating state
change will likely occur near the center of the main barrier beam due to the atom’s
reduced speeds during reflection, maximizing the accompanying potential energy
131
increase. The heating associated with the larger number of devastating scattering
events manifests in the considerable trap losses observed in Figure 4.15.
132
CHAPTER V
COOLING WITH THE ONE-WAY BARRIER
Figures 5.2 and 5.4-5.7 were published in the coauthored work, Ref. [103].
5.1. Introduction
The field of atom optics has risen to prominence on the shoulders of a few,
robust laser-cooling techniques that are astonishingly effective on a handful of atomic
species [36]. Though duly celebrated, these techniques generally require multiple
scattering events to reduce the kinetic energy of an atom, necessitating a cycling
optical transition. In the absence of a reliable cycling transition, atoms decay into
states that are inaccessible to the cooling laser, failing to undergo further cooling.
With a few exceptions [104–109], only a small subset of atoms have an electronic
structure simple enough to meet this requirement, significantly limiting the breadth
of ultra-cold physics research. This creates a need for new, innovative cooling tools
that are applicable to more complex atoms and molecules to broaden the scope of the
research.
One-way-barrier cooling schemes [79, 81, 85, 86, 88, 89, 103] emerge as an ideal
candidate due to the small number of scattering events necessary to achieve cooling.
In principle, only a single scattering event—one that switches the atom from the
133
transmitting to the reflecting state—is required to effect cooling, circumventing the
difficulties arising from the complex electronic structure of many atoms and molecules
[110]. In this chapter we will discuss how one-way-barrier cooling schemes work,
describe our particular implementation, and present our results [103]. We will also
examine the impact of experimental heating effects in general, as well as on the
effectiveness of the cooling process.
5.2. How It Works
The cooling utility of the one-way barrier stems from its ability to compress the
volume of a sample of gas, as described in Section 3.3. Once the barrier has achieved
compression, increasing the volume by slowly translating the barrier cools the gas via
adiabatic, reversible expansion (Fig. 5.1). The term “adiabatic” indicates that no heat
transfer occurs during the expansion, while reversibility requires that the translation
speed of the barrier must be slow compared to the average speed of the gas particles.
For particles in potentials, this is sometimes referred to as adiabatic translation, since
the translation is slow enough that the change in potential experienced by the atom
does not significantly increase its kinetic energy. The expansion cools the gas for the
same reason that adiabatic compression raises the temperature (Section 3.3): The
net entropy change for an adiabatic process is zero, so the entropy increase associated
with the larger volume must be counteracted by an equivalent entropy decrease, which
is manifest in the lower temperature of the gas.
134
Main Barrier 
Beam
1
2
3
Barrier Basics:
Setup
We start atoms in the transmitting state, and have a
second beam pump them into the reflecting state on one
side.
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BarrierBasics:
Setup
Westartatomsinthetransmittingstate,andhavea
secondbeampumpthemintothereflectingstateonone
side.
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Barrier Basics:
Setup
We start atoms in the transmitting state, and have a
second beam pump them i to t e reflecting state on one
si e.
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(a) (b)
Main Barrier 
Beam
3
1
2
Barrier Basics:
Setup
We start atoms in the transmitting state, and have a
second beam pump them into the reflecting state on one
side.
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Barrier Basics:
Setup
We start atoms in the transmitting state, and have a
second beam pump them into the reflecting state on one
side.
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Barrier asics:
Setup
We start ato s in t transmitting state, and have a
second beam pump them into the reflecting state on one
side.
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Repumping 
Barrier Beam
(c) (d)
One-Way Barrier
Reflecting
Transmitting
Reflecting
Transmitting
Figure 5.1. Illustration of how to use the one-way barrier to cool a sample of gas
via adiabatic expansion, modified from an original created by J.J. Thorn.
Though simple in concept, this two-step process (spatial compression followed
by adiabatic expansion) does not speak to the viability of one-way-barrier cooling
schemes. In particular, if the temperature increase suffered during the compression
step is too large, it will negate any cooling benefit derived from the expansion. The
success of this cooling method hinges on the barrier’s ability to decrease the phase-
space volume of the gas during compression. The phase-space volume, which takes
into account changes in both volume and temperature (Section 1.8), will decrease
during the compression process if the effect of the volume compression outweighs any
heating that occurs. Indeed, phase-space volume compression has been demonstrated
with one-way barriers [89, 90, 111], with our results reported in Section 4.5, and
the best result achieved so far yielding a factor of 350 compression from the initial
conditions [111].
A more elegant approach to cooling with the one-way barrier involves combining
the compression and adiabatic expansion steps by confining the gas in a harmonic
potential and sweeping the barrier through the sample (Fig. 5.2) [85]. In this scheme,
135
Figure 5.2. Schematic representation of the one-way-barrier cooling process for a
gas confined in a harmonic potential. Gas particles near their turning points pass
through the barrier and become trapped on the right-hand side, then reduce their
potential energy by following the barrier to the bottom of the potential. This figure
was created by J.J. Thorn.
the harmonic potential governs the motion of the gas particles, which regularly
exchange kinetic and potential energy as they oscillate back and forth in the harmonic
trap. As the one-way barrier is translated from one side of the trap to the other,
gas particles encounter the barrier near their turning points—when they have very
little kinetic energy—becoming trapped by the slowly moving barrier. The trapped
particles proceed to follow the moving barrier to the bottom of the potential, reducing
their potential energy with minimal increase in kinetic energy, cooling the sample of
gas.
The translation speed of the barrier plays a critical role in the effectiveness of
this cooling scheme. For the sweep to be adiabatic, the distance the barrier travels
136
during one oscillation period of the gas particles must be small compared to their
oscillation amplitude. Sweeping the barrier too quickly limits the minimum achievable
temperature of the process by trapping particles away from their turning points,
when they have greater amounts of kinetic energy. It also contributes to unnecessary
heating by increasing the kinetic energy of the already-trapped particles as they “fall”
toward the receding barrier. Treating the particles classically and assuming they
“see” a linear change in the potential over a small translation step of the barrier, the
temperature of a particle when it “catches up” with the barrier is proportional to v 20 ,
where v0 is the translation speed. This implies that the cooling technique becomes
more effective as the translation speed of the barrier is reduced, ignoring spontaneous
emission.
5.3. Experimental Setup
The bulk of the experimental apparatus and procedures for the cooling experiment
remain the same as for the barrier-demonstration experiment (Chapter 4), except for
a few substantial differences which we will detail below.
The primary difference arises from the need to translate the barrier to implement
the cooling scheme. We conveniently mounted the output of the dipole-trap laser
on the air cart (Section 2.5), which allows us to sweep the dipole trap (with the
atoms) through the barrier beams. Translating the barrier beams through the dipole
trap—the approach used in describing the cooling method—would have required
137
considerable changes to the apparatus that were not conducive to its future uses.
Except for the force the atoms experience due to the acceleration and deceleration
of the trapping potential, these two configurations are equivalent, however, provided
the translation is adiabatic.
We originally aligned the dipole-trap beam to intersect the MOT and one of the
dumping mirrors (Section 2.5, Fig. 2.25), which produced a beam that was not parallel
to the table nor to the translation direction of the air cart due to the geometry of
our apparatus. Though this setup sufficed for our one-way barrier experiments, it
proved inadequate for the cooling experiment because translating the air cart shifted
the dipole-trap beam off the dumping mirror and moved the focus of the dipole trap
in all three dimensions (as opposed to just axially), misaligning it with the barrier
beams. In order to implement the cooling experiment, we realigned the dipole-trap
beam parallel to the table and angled the air cart parallel to the beam path that
intersected the dumping mirror (Fig. 5.3).
These changes enabled us to translate the dipole-trap without compromising its
alignment with the barrier beams or the dumping mirror; however, they produced a
new set of technical challenges. In particular, the low height of the dumping mirrors
forced the dipole-trap beam to pass far below the standard MOT position near the
center of the Hellma cell (Fig. 5.3), requiring us to load the dipole trap uncomfortably
close to the bottom of the cell (about 4.2 mm above it). So close, in fact, that there
was insufficient MOT-trapping and repump light to form a MOT at that low of a
138
Dipole-Trap
Beam Spherical
Cube
MOT
Air Cart
Mirror
Hellma Cell
Side View
(a)
Air Cart
Dipole-Trap
Beam
Hellma Cell
Mirrors
Spherical
Cube
MOT
Top View
(b)
(parallel to beam)
Figure 5.3. Schematic diagram showing the alignment of the dipole-trap beam
with the MOT and the dumping mirrors for the one-way-barrier cooling experiments,
including the air cart, dipole-trap beam, Hellma cell, MOT, spherical cube and
dumping mirrors. Figure 2.25 shows the previous alignment for the one-way-barrier
demonstration experiments. (a) Side view illustrating how the dipole-trap beam must
pass close to bottom of the Hellma cell to be parallel with the optical table. (b) Top
view illustrating the orientation of the air cart to ensure the translation direction is
parallel to the dipole-trap-beam direction.
position. To remedy this, we shifted the MOT beams down by 3/16′′, and adjusted
the Helmholtz and anti-Helmholtz coil values to form a strong, fast-loading MOT
lower in the cell (referred to as the “new position”), though still higher than the
dipole-trap position.
Changing the beam positions affected several other aspects of the experiment.
First, to image the atoms effectively, we had to lower the height of the absorption
139
imaging beam and the camera. Second, we had to angle the barrier beams downwards
using the steering mirror (mirror 2) to overlap them with the dipole-trap focus. The
most significant effect, however, was on the MOT and dipole-trap loading procedures.
In the case of the MOT, we were no longer able to use the trick of loading the MOT
up high in the atomic beam (Section 4.2) to bolster the atom numbers, as the MOT
beams were now too low to form a MOT at that height. Unfortunately, this reduced
the number of atoms we were able to load into the dipole trap. For loading the
dipole trap, the lowered MOT beams provided enough light to form a MOT near its
focus, but the MOT was too weak to efficiently load the dipole trap. As a result, we
loaded the MOT in the new position (which was still much higher than the position
of the dipole trap), then rapidly shifted the MOT to the dipole-trap position with the
magnetic bias fields for loading. Though the size of the MOT decayed at this lower
position, the time scale for the decay was much longer than the loading time of the
dipole trap.
Aside from the lower position, the dipole-trap parameters remained the same as
reported previously (Section 4.2). This includes the operating power, beam waist,
trap depth, and oscillation frequencies.
To carry out the cooling experiment, we load the MOT for 7 s at the new
position, trapping approximately 1.4 × 105 atoms at about 30 µK. We then shift
the MOT 0.95(5) mm left of the dipole-trap focus with the magnetic bias fields for
loading. Loading off to the side improves the loading efficiency as well as effectively
140
increases the initial temperature of the dipole-trapped atoms. Heating the atoms
prior to the measurement ensures the initial ensemble is much warmer than the lowest
temperature achievable with our setup, which is significantly limited by experimental
constraints and heating effects (see Sections 5.6 and 5.7). We load the dipole trap for
110 ms, filling it uniformly with about 8×104 atoms at a temperature of approximately
110 µK, then leave the MOT light on for an extra 15 ms to optically pump the atoms
to the F = 1 ground state. Next we modulate the intensity of the dipole-trap laser
using a square wave with a 24 ms period, switching between 100% and 120% of the
nominal operating power for 100 periods. The modulation heats the atoms further via
parametric excitation [112], resulting in approximately 4×104 atoms at a temperature
of about 170 µK in the dipole trap.
The geometry of the one-way barrier remains largely intact (Section 3.4), except
we increased the beam separation to 36(1) µm to minimize heating on the reflecting
side of the barrier. We also reduced unwanted heating by lowering the power of the
main barrier beam to 24(2) µW, since the atoms trapped by the barrier have very
little kinetic energy and therefore do not require as high a potential barrier. The
repumping-barrier-beam power remains relatively unchanged at 0.34(3) µW. Both
beams were left linearly polarized perpendicular to the dipole-trap axis, and the other
barrier-beam parameters remain the same as reported previously (Section 3.5).
As mentioned in Section 5.2, the adiabatic-translation requirement dictates that
the sweep speed of the barrier must be slow compared to the average speed of the
141
oscillating atoms. After heating, the average speed of an atom in the dipole trap
during one oscillation period is roughly 100 mm/s, so we want a translation speed
at least an order of magnitude smaller. Additionally, we remained cognizant of the
limited trap lifetimes in the presence of the barrier (about 700−900 ms), which inhibit
us from selecting an arbitrarily slow sweep speed. These considerations informed our
choice of a 5 mm/s translation speed, which we reasoned would provide a balance
between improved cooling and atom loss due to scattered light from the barrier beam.
Section 5.5 examines how the translation speed affects the performance of the cooling
scheme in detail.
The series of steps to execute the cooling experiment is as follows: First, the atoms
are loaded into the dipole-trap and optically pumped to the F = 1 transmitting state
with the air cart at the location where the dipole-trap focus intersects the main barrier
beam. Next, we translate the trap 2.5 mm to the left of the barrier position (as seen
by the camera) at 5 mm/s (Fig. 5.4). During this movement, we heat the atoms via
dipole-trap intensity modulation for 2400 ms then turn on the barrier beams. At
time t = 0, we translate the air cart 1.5 mm to the right of the barrier position at a
speed of 5 mm/s. We begin recording images 290 ms after the sweep starts, just as
the atomic cloud starts to pass through the barrier. We continue to record images
every 30 ms until about 500 ms after the air cart has come to rest (Fig. 5.4). We note
that the atoms are still in motion when many of the images are taken, and that each
measurement is destructive, so we repeat the series of events for each image.
142
BRIEF ARTICLE
THE AUTHOR
barrier position
loading
position
sweep start
pictures
begin
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t = −2660 ms
t = 0 ms
t = 290 ms
t = 810 ms
-2.5
0
2.5
(mm)
1
BRIEF ARTICLE
THE AUTHOR
barrier position
loading
position
sweep start
pictures
begin
final
continue
t = −2660 ms
t = 0 ms
t = 290 ms
t = 810 ms
-2.5
0
2.5
(mm)
1
I I
E
barrier position
loading
position
s eep start
pictures
begin
final
continue
t 2660 s
t 0 s
t 290 s
t 810 s
-2.5
0
2.5
( )
1
BRIEF ARTICL
THE AUTHOR
barrier position
loading
position
sweep start
pictures
begin
final
continue
t = −2660 ms
t = 0 ms
t = 290 ms
t = 810 ms
-2.5
0
2.5
(mm)
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barrier position
loading
position
sweep start
pictures
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t = −2660 ms
t = 0 ms
t = 290 ms
t = 810 ms
-2.5
0
2.5
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loading
position
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t = −2660 ms
t = 0 ms
t = 290 ms
t = 810 ms
-2.5
0
2.5
(mm)
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barrier position
loading
position
swe p start
pictures
begin
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t = −266 s
t = 0 ms
t = 90 ms
t = 810 ms
-2.5
0
2.5
( m)
1
BRIEF ARTICLE
THE AUTHOR
barrier position
loading
position
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pictures
begin
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t = −2660 ms
t = 0 ms
t = 290 ms
t = 810 ms
-2.5
0
2.5
(mm)
1
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THE AUTHOR
barrier position
loading
position
sweep start
pictures
begin
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t = −2660 ms
t = 0 ms
t = 290 ms
t = 810 s
-2.5
0
2.5
(mm)
1
BRIEF ARTICLE
THE AUTHOR
barrier position
loading
position
sweep start
pictures
begin
final
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t = −2660 ms
t = 0 ms
t = 290 ms
t = 810 ms
-2.5
0
2.5
(mm)
1
BRIEF ARTICLE
THE AUTHOR
barrier position
loading
position
sweep start
pictures
begin
final
con inue
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t = 0 ms
t = 290 ms
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-2.5
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loading
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t = −2660 ms
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t = 290 ms
t = 810 ms
-2.5
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barrier position
loading
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swe p start
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t = −2660 ms
t = 0 s
t = 290 ms
t = 810 ms
-2.5
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(mm)
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barrier position
loading
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t = −2660 s
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t = 290 ms
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(mm)
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ARTICLE
TH AUTHOR
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-2.5
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HE AUTHOR
barrier position
loading
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t = −2660 ms
t = 0 ms
t = 290 ms
t = 810 ms
-2.5
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2.5
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barrier position
loading
position
sweep start
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t = −2660 ms
t = 0 ms
t = 290 ms
t = 810 ms
-2.5
0
2.5
(mm)
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BRIEF AR ICLE
THE AUTHOR
barrier position
loading
osition
sweep start
pictures
begin
final
continue
t = −2660 ms
t = 0 ms
t = 290 ms
t = 810 ms
-2.5
0
2.5
(mm)
1
Figure 5.4. Illustration of the dipole-trap translation and imaging sequence. The
times shown correspond to a translation speed of 5 mm/s.
5.4. Demonstrating Cooling
The atomic spatial distributions in the dipole trap during the sweep in the presence
and absence of the one-way barrier are presented in Figure 5.5. The barrier is located
at the origin of the plot and the hot atomic distributions are translated through the
barrier from left to right. At time t = 290 ms, the warmest atoms in the sample
just start to encounter the barrier, becoming trapped on its right-hand side. These
trapped atoms appear as a small peak in the data with the barrier, visible to the right
of the barrier position. The peak continues to grow as the translation progresses, since
more atoms become trapped near their turning points, evidenced by the larger peak
in the atomic distribution at time t = 440 ms. The trapped atoms reduce their
potential energy by adiabatically following the barrier to the bottom of the potential,
143
with minimal increase in their kinetic energy. All the atoms have become trapped
by the time the center of the dipole-trap passes through the barrier, which slowly
expands the cooled, asymmetric distribution in the harmonic potential. This stage
of the cooling process is captured in the atomic distribution with the barrier at time
t = 590 ms. It is important to note that the width of the spatial distributions does not
accurately reflect the temperature when the barrier is in contact with the atoms (as it
is for the data at t = 440 ms and 590 ms), because the harmonic dipole-trap potential
is effectively cut in half by the one-way barrier potential. The spatial distributions
at t = 740 ms and 890 ms demonstrate the cooling effect of the sweep, manifest
in their narrower widths as compared to the distributions without the barrier. We
believe several possible heating mechanisms are responsible for the slow increase in
temperature (width) observed at times t = 1040 ms and t = 1190 ms, where the
cooling effect of the barrier becomes less obvious. Section 5.7 contains an in-depth
discussion of the possible heat sources contributing to this warming effect.
Figure 5.6 shows the width of the atomic ensemble before, during and after the
cooling process with and without the barrier, measured as the FWHM of the spatial
distributions presented in Figure 5.5. The vertical line marks the time when the
translation has finished. Prior to this time, the width is not an appropriate indicator
of temperature for the distributions with the barrier because it is still interacting
with the atoms, as mentioned previously. After completing the sweep, the atoms are
cooled to about 100 µK, reflecting a factor of 1.7 reduction in the temperature after
144
290.0 ms
440.0 ms
590.0 ms
740.0 ms
890.0 ms
1040.0 ms
1190.0 ms
-3 0 3
position (mm)
p
o
p
u
la
ti
on
 (
ar
b
. 
u
n
it
s)
Figure 5.5. Atomic distributions in the dipole trap during translation with (black
curves) and without (gray curves) the one-way barrier. The barrier beams are located
at position zero. Each curve is an average of 16 repetitions of the experiment,
smoothed slightly for clarity.
cooling in one dimension. This corresponds to a factor of 1.7 reduction in the phase-
space volume when accounting for the spatial compression and temperature change.
Previous work for an earlier one-way-barrier cooling scheme reported greater phase-
space compression [111], however, we note that the two experimental realizations
are substantially different. First, Bannerman et al. employed a magneto-optical
configuration, transferring atoms from a magnetic trap into an optical trap, while
we demonstrated an all-optical realization, which requires higher powers and more
145
500 750 1000 1250
0
1
2
3
time (ms)
w
id
th
 (
m
m
)
with barrier
without barrier
Figure 5.6. The FWHM of the spatial distribution in the dipole trap as a function of
time during the translation with (squares) and without (circles) the one-way barrier.
The times are measured from the start of the sweep and the vertical line delineates
the time when the sweep has finished. The error bars indicate the standard deviation
for the average of 16 repetitions of the experiment.
scattering events. Second, we cool nearly 100% of the atoms initially loaded into the
dipole trap, while they report a 0.3% transfer efficiency between the magnetic trap
and the optical trap [111]. Our implementation ought to perform better, though,
as simulations of the cooling process reveal that a factor of nine cooling should be
achievable. We believe the origin of this discrepancy comes from the previously
mentioned heating effects counteracting the cooling process, which are also manifest
in the slow increase in temperature observed in Figure 5.6 after the sweep has ended.
146
5.5. Effect of Translation Speed
As discussed earlier (Section 5.3), we expect the efficiency of the cooling scheme
to improve as we reduce the barrier’s translation speed through the trap. However,
experimental realities for our implementation also indicate that translating the barrier
too slowly will result in increased heating due to scattering in the presence of the
barrier (Section 4.4). Figure 5.7 shows the width of the atomic distribution after
passing through the barrier for several different sweep speeds. The data appear in
two different sets (circles and squares) due to the large deceleration distances that
accompany the high translation speeds. In particular, we want to prevent the air
cart from starting to decelerate while the barrier is in contact with the atomic sample
to ensure that the entire sweep is completed at a constant velocity. As a result,
the data represented by the circles were taken while the air cart passed 1.5 mm at
constant velocity. The data represented by the squares have velocities slow enough
that the images were taken as the air cart decelerated to rest at a position of 1.5 mm.
These two data sets partially overlap, which raises some concerns about timing. In
particular, to accurately compare the cooling effects at the same velocity under the
different experimental conditions (constant velocity versus decelerating at the time
of the image), it is imperative that the length of time between passing through the
barrier and taking the image coincides as closely as possible for each velocity. This
concern arises from the additional heating that occurs while the atoms reside in the
dipole-trap after completing the sweep, which increases the width of the distributions
147
over time. To address this concern, the images represented by the squares were taken
at times that matched the constant-velocity data (circles) as closely as possible. The
overlap in the two data sets also provides us valuable insight into the effects of the
air-cart motion on the temperature of the atoms. The good agreement between the
overlapping data points indicate that no discernible heating can be attributed to the
deceleration of the air cart. For velocities above 25 mm/s in Figure 5.7, we observe
a rapid increase in the width of the atomic distribution, which is consistent with the
expectation that at high speeds the translation ceases to be adiabatic. The width
of the distribution after the sweep narrows at lower velocities, reaching a minimum
at about 10 mm/s. Below this velocity, the widths begin to increase again as the
atoms spend longer amounts of time trapped against the barrier, scattering more
barrier-beam light that heats the atomic sample.
5.6. Limitations
Several factors resulting from our particular implementation limit the effectiveness
of this cooling scheme. First, we treat the system as effectively one-dimensional
because the single-beam, far-detuned dipole trap results in disparate longitudinal
and radial oscillation frequencies (Section 4.2). Simulations reveal, however, that the
transverse dimensions can contain a substantial amount of kinetic energy [78]. Our
work is limited by the fact that we exclusively cool the atoms in the longitudinal
dimension.
148
0 10 20 30 40 50
1.5
2.0
2.5
speed (mm/s)
w
id
th
 (
m
m
)
Figure 5.7. The width of the atomic distribution in the dipole trap as a function
of translation velocity, measured after passing through the barrier. The circular
data points represent measurements taken as the air cart passed 1.5 mm at constant
velocity, while the square data points represent measurements taken as the air cart
came to rest at 1.5 mm. Each square (circular) data point corresponds to the average
of 16(6) repetitions of the experiment, with the error bars indicating the standard
deviation.
The relatively small hyperfine ground-state splitting of 87Rb, which constituted
the main experimental challenge throughout our one-way barrier work, imposes the
second, significant limitation inherent in our experiment. As discussed on several
occasions (Section 3.4, 4.4, 4.6.1, and 4.6.4), the atoms undergo an excessive number
of scattering events when interacting with the barrier due to the restricted detunings
afforded by the hyperfine ground-state splitting, leading to heating and trap losses
that limit the lifetimes in the presence of the barrier. For example, the moving barrier
produces about 3 scattering events during transmission and around 4 scattering events
during reflection. This has serious implications for the effectiveness of this cooling
scheme, as it requires repeated reflections from the barrier to cool the atoms during
149
the adiabatic translation process. In particular, the excessive scattering prevents
us from sweeping the barrier arbitrarily slowly, because at some point the heating
and trap losses will overcome any cooling benefit derived from the slower translation
speed. We observe evidence of this limit in Figure 5.7.
Increasing the frequency difference between the transmitting and reflecting states
to allow for larger detunings stands out as the most obvious improvement to this
cooling scheme. Section 4.4 mentions several ways to accomplish this, ranging from
utilizing the fine structure of 87Rb to realizing the cooling technique with a different
atomic or molecular species that has a more versatile level structure. Clearly, applying
this cooling method to a new atom or molecule warrants careful consideration of the
atomic structure and the detuning of the main barrier beam.
5.7. Anomalous Heating
As alluded to in Section 5.4, our one-way-barrier cooling experiment successfully
reduces the temperature of the atomic ensemble, only to have the cooling gains slowly
eroded as the atoms reside in the dipole trap after the sweep. This increase in
temperature, visible in Figures 5.5 and 5.6 as the widening of the atomic distributions,
makes up most of the temperature difference between the cooled and uncooled samples
in about the first 700 ms after the sweep has finished. Figure 5.8 shows the width of
the atomic distribution as a function of time for atoms with and without the barrier
for several seconds after a 10 mm/s sweep. It is clear that after their initial reduction
150
with barrier
no barrier
0 1000 2000 3000 4000
1.6
1.8
2.0
2.2
2.4
time (ms)
w
id
th
 (
m
m
)
Figure 5.8. The width of the atomic distribution in the dipole trap for atoms
translated at 10 mm/s with (blue) and without (red) the one-way barrier for several
seconds after the sweep has finished. The error bars represent statistical error for 16
repetitions of the experiment.
in temperature, the atomic sample starts to warm, eventually reaching close to a
steady-state temperature (there is a slow linear increase) almost equivalent to the
uncooled sample after about 3.5 s. This perplexing behavior mandates that energy is
either being added to the system or redistributed by some means, though the cause
is not immediately obvious. Below we will detail our efforts to track down the source
of this anomalous heating.
Examining our system, we determined three potential heating sources: the one-
dimensional nature of our cooling scheme, the barrier, and the air-cart motion. In
the case of the first, we know that significant amounts of energy can be present
in the transverse dimensions [78], such that any anharmonic coupling between the
151
longitudinal and radial degrees of freedom could redistribute some of the transverse
kinetic energy to the longitudinal dimension after the sweep. Should this be the case,
sweeping the barrier through the atoms twice should reduce the final temperature
of the ensemble, provided the sweep does not add the same amount of energy back
into the system. Figure 5.9 shows the width of the atomic distribution as a function
of time after one and two sweeps through the barrier at a velocity of 10 mm/s. We
see that immediately after completing the sweep(s) (time t = 0), the ensemble that
passes through the barrier twice is a little bit cooler, then quickly warms to a (near)
steady-state temperature slightly lower than the one-sweep sample. It is important
to note that the time the atoms reside in the dipole trap before the second sweep
is about 600 ms, such that their temperature prior to the second sweep is close to
the (near) steady-state value achieved after one sweep. These data suggest that a
small amount of the heating can be attributed to anharmonic coupling between the
cooled and uncooled degrees of freedom, evidenced by the slightly narrower width of
the atomic distribution after completing two sweeps through the barrier (Fig. 5.9).
Our previous work with the one-way barrier indicates that the separation of the
barrier beams and their depth of focus (z-direction, Fig. 3.11) alignment with the
dipole-trap focus affect the number of expected scattering events, and thus heating
due to contact with the barrier. To this end, we doubled the separation of the barrier
beams to 65 µm, and repeated the experiment with the same parameters used to
collect the data in Figures 5.5 and 5.6. Increasing the separation had no discernible
152
2 sweeps
1 sweep
0 1000 2000 3000 4000
1.4
1.6
1.8
2.0
2.2
2.4
time (ms)
w
id
th
 (
m
m
)
Figure 5.9. The width of the atomic distribution after completing one (blue) and
two (red) sweeps through the barrier as a function of time for v = 10 mm/s. The
error bars represent statistical error for 16 repetitions of the experiment.
impact on the width of the atomic distribution, as the data mimicked that collected
for the smaller separation.
To address the alignment issue, we meticulously realigned the foci of the barrier
beams with the dipole-trap focus using the method outlined in Section 3.7. We
calculated that about a 0.5 mm offset in the z-direction places the barrier foci about
one Rayleigh length (∼0.53 mm) away from the dipole-trap focus due to their small
beam waists in the longitudinal direction. At one Rayleigh length away from the
foci, the waist of the barrier beams increases by about 40%, revealing that even
small displacements can substantially increase the width of the barrier beams at
the position where they intersect the dipole trap. We determined that we were off by
153
about 0.38 mm, likely resulting from the major repositioning of the air cart and dipole-
trap beam necessary to perform the one-way-barrier cooling experiment. However,
the data collected after the realignment showed no appreciable improvement in the
final temperature of the atomic distributions despite the more precise alignment. We
note, however, that some uncertainty in the overlap of the dipole-trap beam with the
barrier beams persists as our alignment method limits us to a resolution of roughly
0.34 mm. Considering this, we cannot rule out the possibility that uncertainty in the
alignment may contribute to the heating. It is worthwhile to acknowledge that there
is no compelling reason to assume these possible heating mechanisms play a role in
the heating that occurs after the sweep has concluded, when the atoms are no longer
in contact with the barrier. However, in an effort to understand and characterize the
problem, we felt it prudent to investigate all potential heating sources.
The motion of the air cart generates some concern in the context of the heating
effects, particularly because we are actually moving the atoms as opposed to the
barrier beams. Of particular concern is the deceleration of the air cart as it comes
to rest after the sweep, which can potentially impart energy to the atoms, or vibrate
the air cart or the affixed optics at a frequency that heats the atoms. Vibrations that
could cause heating should have a period close to the longitudinal oscillation period
of the atoms in the dipole trap (about 50 ms, or 20 Hz) [113], and must occur over
a time period of several hundred milliseconds to account for the heating observed in
Figure 5.8.
154
The nominal deceleration (and acceleration) of the air cart is 500 mm/s2, though
we have the ability to change it with the computer. We used the same method to test
for longitudinal vibrations of both the air cart and the attached optics, which involved
affixing a razor blade to the equipment of interest, which then partially intercepted
a laser beam focused onto a photodiode as the air cart came to rest. Figure 5.10
shows the measured laser power as a function of time for two different accelerations
(a = 100 and 500 mm/s2) at three different velocities (v = 5, 10 and 20 mm/s), with
the razor blade attached to the air cart. The two horizontal lines indicate the laser
intensity for two different air-cart positions separated by 10 µm, which provide a scale
for the amplitude of the vibrations. We observe a distinct vibration with a period of
about 40 ms as the air cart comes to rest for all speeds and accelerations; however the
amplitude is much greater when the acceleration is 500 mm/s2. Though the vibration
period falls in the range necessary for heating, we see that all the vibrations rapidly
damp away after about one oscillation period, regardless of their amplitude. The data
produced with the razor blade attached to the optics (as opposed to the air cart) look
nearly identical, indicating that the optics are fixed rigidly to the air cart. These data
suggest that neither longitudinal vibrations of the air cart nor the affixed optics are
responsible for any significant heating over the time scale of interest.
To look for signs that the air cart imparts energy to the atoms during the de-
celeration process, we took images of the atoms in the dipole trap as the air cart
came to rest (no barrier) for the same velocity and acceleration combinations used
155
Power w/ cart at 86.69 mm
Power w/ cart at 86.70 mm
v=20 mm/s, a=500 mm/s €
v=20 mm/s, a=100 mm/s €
v=10 mm/s, a=500 mm/s €
v=10 mm/s, a=100 mm/s €
v=5 mm/s, a=500 mm/s €
v=5 mm/s, a=100 mm/s €
0 0.05 0.1 0.15 0.2
time (s)
tr
an
sm
it
te
d
 p
ow
er
 (
ar
b
. 
u
n
it
s)
Figure 5.10. The power reaching a photodiode (measured on an oscilloscope) as
the air cart comes to rest, partially blocking a laser beam with an attached razor
blade. The data show all six combinations of the air-cart’s velocity for v = 5, 10 and
20 mm/s and acceleration for a = 100 and 500 mm/s2. The two horizontal traces
delineate the power for two air-cart positions separated by 10 µm, which provides a
distance scale for the observed vibrations.
in the vibration tests. Figure 5.11 presents the results, showing the position of
the center of the atomic distributions as a function of time for 250 ms after the
translation has ended. We observe that the atoms exhibit some collective oscillation
about the center of the dipole trap for the 500 mm/s2 acceleration at the higher
velocities, which damps away after about 200 ms. This collective motion is markedly
reduced for the slower-acceleration and lower-velocity data, however, indicating that
the deceleration process does impart some energy to the atoms, the amount of which
depends on the acceleration and velocity of the air cart. To assuage our concerns
156
v=20 mm/s, a=500 mm/s €
v=20 mm/s, a=100 mm/s €
v=10 mm/s, a=500 mm/s €
v=10 mm/s, a=100 mm/s €
v=5 mm/s, a=500 mm/s €
v=5 mm/s, a=100 mm/s €
0 50 100 150 200 250
5.2
5.3
time (ms)
ce
n
te
r 
p
o
si
ti
on
 (
m
m
)
Figure 5.11. The center position of the atomic distribution in the dipole trap after
the air cart has come to rest as a function of time. The data show all six combinations
of the air-cart’s velocity for v = 5, 10 and 20 mm/s and acceleration for a = 100
and 500 mm/s2. The error bars represent statistical error for 14 repetitions of the
experiment.
about the effects of the air-cart acceleration, we collected data on the width of the
atomic distribution after the air cart came to rest from a velocity of 5 mm/s with an
a = 100 and 500 mm/s2 deceleration (Fig. 5.12). The two different sets of data are
indistinguishable, leading us to conclude that the motion and acceleration of the air
cart have no impact on the heating effects observed in our system.
While working on diagnosing the cause of the anomalous heating, we discovered
that loading the atoms at the center of the dipole trap produced an ensemble with
an initial width comparable to the width of the atomic sample immediately after
passing through the barrier. To our surprise, we also discovered that these atoms
157
ao=o500 mm/s € (blue)
ao=o100 mm/s € (red)
0 500 1000 1500
1.4
1.6
1.8
2.0
2.2
2.4
2.6
time (ms)
w
id
th
 (
m
m
)
Figure 5.12. The width of the atomic distribution after the air cart has come to
rest as a function of time for an acceleration of 100 (red) and 500 mm/s2 (blue) and
a velocity of 5 mm/s. The error bars represent statistical error for 12 repetitions of
the experiment.
suffer a similar increase in temperature while residing in the dipole trap, despite the
absence of the barrier or any air-cart motion. Figure 5.13 compares the width of the
atoms as a function of time for a sample swept through the barrier once and a sample
simply loaded in the center of the dipole trap. The time scale of the width increase
for the center-loaded atoms is a little smaller (about 500 ms, measured from data not
shown here), and the sample warms to a lower (near) steady-state temperature (it
too, exhibits a slow, linear increase thereafter) than that of the atoms that interact
with the barrier. This discovery reveals that while the barrier/air-cart motion does
contribute some to the anomalous heating, a major component of this phenomenon
must have nothing to do with the cooling process or its associated mechanics, but
158
1 sweep, 10 mm/s
center-loaded,
no barrier or sweep
0 200 400 600 800 1000 1200
1.4
1.6
1.8
2.0
2.2
time (ms)
w
id
th
 (
m
m
)
Figure 5.13. The width of the atomic distribution as a function of time for atoms
loaded into the center of the trap with no barrier or air-cart movement (blue) and
for atoms swept through the barrier once at 10 mm/s (red). The error bars for
the no-sweep (sweep) data represent statistical error for 14 (16) repetitions of the
experiment.
instead results from our general experimental setup or the dipole-trap laser and its
interaction with the atoms. Indeed, several experiments using dipole traps have
reported unexplained heating effects as well [114–117].
When considering heating sources associated with our experimental setup and the
dipole-trap laser, several possibilities come to mind. These include vibrations of the
fiber that connects to the dipole-trap laser’s collimator, stray light, dipole-trap-laser
intensity fluctuations, dipole-trap loading power, dipole-trap operating power, lensing
through the Hellma cell due to heating of the fused silica by the dipole-trap laser, a
fluctuating spatial-mode structure, and spectral components of the dipole-trap laser
159
that could drive the hyperfine transitions in 87Rb. In the next several paragraphs
we will outline our efforts to characterize the problem and test these possibilities,
recalling that we are generally looking for vibrations, fluctuations, and oscillations
with a period of about 50 ms (20 Hz) if they shift the position of the trap focus,
or some multiple of that frequency for the intensity fluctuations [113]. Additionally,
these disturbances must occur over a time scale of several hundred milliseconds.
It is also worth noting that we measured the lifetime of the atoms in the dipole-
trap in its new configuration near the bottom of the Hellma cell to be about 5 s.
This was substantially lower than the 20 s measured previously during the one-way-
barrier demonstration experiments, causing us some concern. In particular, shifting
the location of the dipole-trap beam ought to have no effect on the lifetimes, which
should depend on the background pressure and the rate of light-induced collision
losses. In an effort to improve the lifetimes, we sealed off the rubidium source for
a while and ran the Ti-sublimation pump and getters several times. The lifetime
showed a modest improvement from about 5 s to 12 s, which may have improved a
little more had we purged the chamber longer, though it is not clear how close we
would have gotten to 20 s. Additionally, the lifetime data clearly exhibited a slow,
linear increase in the distribution widths after the much more rapid increase observed
in the first 500 ms, as alluded to earlier. We consider this slow increase in width
(about 12 µm/s) a result of the atoms scattering dipole-trap laser light [47], though
pointing instabilities in the dipole-trap laser could contribute to this as well [113].
160
The main concern regarding vibrations of the dipole-laser’s fiber arise from the
HEPA air filter that is mounted above the optics table in an overhead platform.
Though the platform is isolated from the optics table, it supports a metal rod that
contacts the fiber, exposing the fiber to vibrations from the filter. The dipole-trap
fiber was originally loosely Scotch taped to this metal bar, so we attempted to damp its
contact with the bar by inserting some sorbothane for padding and suspending it with
a string. This appeared to make the heating worse, increasing the width after 1 s by
roughly 60 µm, so we tried turning the HEPA filter off altogether. This made matters
worse yet, adding roughly another 15 µm to the width. Subsequent adjustments to
the fiber contact never returned the resulting heating back to the levels seen before
altering it, and we eventually settled on securing the fiber directly to the metal
bar with masking tape (similar to the original arrangement), which produced data
closer to what we had initially observed. Additionally, we also tested for transverse
vibrations of the fiber by reflecting the beam onto a the edge of a photodetector. We
observed no changes in the intensity over the time scales of interest, even when when
tapping on the fiber housing, leading us to conclude that transverse vibrations are
not a significant heating mechanism.
Next we blocked all sources of stray light from reaching the Hellma cell by shut-
tering all the lasers and surrounding the entire vacuum chamber with large pieces of
cardboard. Unfortunately, this had no impact on the heating effects.
To measure fluctuations in the dipole-trap intensity while the atoms resided in the
161
dipole-trap, we picked off part of the beam before it entered the beam dump (after
exiting the vacuum chamber) and sent it into a photodetector. This allowed us to
document any intensity changes actually experienced by the atoms during the various
steps of the experiment. We observed distinct, slow fluctuations during the first 2.5 s
after turning the dipole-trap on, whose period lengthened from about 20 to 270 ms
during that time before finally subsiding. To investigate if these slow fluctuations have
any effect on the heating, we turned the dipole trap on during the 7 s MOT-loading
time (the MOT loads above the location of the dipole trap, so this did not affect
the loading MOT) to ensure these fluctuations had dissipated by the time the atoms
were loaded into the dipole trap. This change, however, did not affect the observed
heating phenomenon. Incidentally, this also provided a convenient test to determine
if heating from the dipole-trap laser expands the fused-silica end of the Hellma cell,
shifting the beam waist and focus: turning the dipole-trap laser on several seconds
prior loading the atoms into the dipole-trap ensures that any expansion of the fused
silica has reached a steady state. These data also confirm that this mechanism is not
responsible for the observed heating.
We also examined the power spectrum of our dipole-trap-laser intensity data to
look for suspicious frequency components. This analysis uncovered a small, trouble-
some peak at 40 Hz in the data collected after the atoms were heated via parametric
excitation, significant enough to merit concern that it may contribute to the heating
effects. The amplitude of this oscillation is quite small compared to the dipole-trap
162
operating power, however, so it likely does not contribute significantly to the heating.
Unfortunately, we were unable to verify this experimentally, as controlling intensity
fluctuations at this frequency would require us to implement a feedback-controlled
intensity-stabilization scheme that we were not prepared to pursue.
We investigated the effects of the dipole-trap loading and operating power by
observing the width of the atomic distribution for center-loaded atoms for all the
combinations of 10, 15, and 19 W loading and operating powers. Figure 5.14 presents
the data, which reveal a couple of noteworthy results. First, it appears that the
loading power has some influence on the initial temperature of the sample, with higher
loading powers yielding warmer atoms. This intuitively makes sense in that at higher
loading powers, atoms may enter the trap with larger transverse energies due to the
greater trap depth in the radial dimensions, which then couples to the longitudinal
dimension. We also observe that the atoms warm at similar rates despite the different
loading and operating powers. Though the data indicate that the loading power can
affect the initial temperature of the sample, it is not clear that it has any appreciable
impact on the subsequent heating.
Our beam-waist measurements for the dipole-trap indicate a spatial profile similar
to a Gaussian, though we did not collect any detailed data on the beam profile nor
test its stability. As a result, we are unable to establish the existence and examine
the effects of this potential heating mechanism.
163
10 W load, 10 W hold
10 W load, 15 W hold
10 W load, 19 W hold
15 W load, 10 W hold
15 W load, 15 W hold
15 W load, 19 W hold
19 W load, 10 W hold
19 W load, 15 W hold
19 W load, 19 W hold
0 200 400 600 800
1
2
3
time (ms)
w
id
th
 (
m
m
)
Figure 5.14. The width of the atomic distribution as a function of time for atoms
loaded into the center of the trap for the nine combinations of 10, 15, and 19 W
dipole-trap loading powers and 10, 15, and 19 W dipole-trap operating powers. The
error bars represent statistical error for 6 repetitions of the experiment.
We attempted to test for a 6.8 GHz frequency component (the D2 hyperfine ground
state splitting) in the dipole-trap beam using a 25 GHz photodiode and a sampling
oscilloscope, but the signal was too noisy to rule out the possibility. A spectrum
analyzer would likely be a better tool for this measurement, however at that time
we did not have access to one. As a result, we cannot eliminate the possibility that
the dipole-trap laser drives transitions between the two ground states, though we
acknowledge that the likelihood of this is low.
We conclude that several factors likely contribute to the anomalous heating of the
atomic sample observed after completing the sweep, including anharmonic coupling
164
to the uncooled, transverse degrees of freedom, uncertainty in the overlap of the
dipole-trap focus with the foci of the barrier beams, dipole-trap intensity fluctuations,
scattering of dipole-trap light amplified by light-assisted collisions, and possibly spa-
tial mode fluctuations and non-trivial frequency components in the dipole-trap laser.
165
CHAPTER VI
CONCLUSION
In summary, we implemented and demonstrated an all-optical one-way barrier
with the ability to direct atomic motion and compress the phase-space volume of a
sample of neutral alkali atoms. We investigated its response to variations of several
key experimental parameters, concluding that the barrier remains quite robust to
mechanical and optical changes. We also implemented a novel cooling scheme that
involved translating the barrier through a warm sample of atoms and demonstrated
its effectiveness at cooling and compressing the atomic sample.
We addressed the limitations of the one-way barrier and the related cooling
scheme, noting that the main obstacles stem from an anomalous heating effect and our
particular implementation with 87Rb. For this atom, the relatively small ground-state
splitting results in an excessive amount of scattering in the presence of the barrier,
limiting the trap lifetimes. We also examined several improvements to address the
scattering problem, which generally involved increasing the detuning between the
main barrier beam and the atomic states.
The future directions of this work are two-fold, with one aspect focusing on
mitigating the scattering problem, while the other aspect is more application oriented.
Possible avenues for improving the barrier’s performance involve implementation
166
utilizing the fine structure of 87Rb, as well as implementation with a different atomic
or (possibly) molecular species. Progress on this front will bolster the application-
oriented work, making the one-way barrier a more attractive tool for use in atom-
chip technology. Additionally, demonstration of a one-way barrier with a previously
uncooled atom or molecule opens the door for applications as a new cooling tool for
atoms and molecules not amenable to standard laser-cooling techniques.
167
BIBLIOGRAPHY
[1] J. C. Maxwell, A Treatise on Electricity and Magnetism (1st Ed, Oxford, 1873).
[2] P. N. Lebedev, “The Experimental Study of the Pressure of the Light,” Annalen
der Physik 4, 29 (1901).
[3] E. F. Nichols and G. F. Hull, “A Preliminary Communication on the Pressure
of Heat and Light Radiation,” Physical Review (Series I) 13, 307 (1901).
[4] E. F. Nichols and G. F. Hull, “The Pressure Due to Radiation. (Second Paper.),”
Physical Review (Series I) 17, 26 (1903).
[5] E. F. Nichols and G. F. Hull, “The Pressure Due to Radiation. (Second Paper.),”
Physical Review (Series I) 17, 91 (1903).
[6] D. J. Wineland and H. G. Dehmelt, “Proposed 1014 Delta Upsilon Less Than
Upsilon Laser Fluorescence Spectroscopy on T1+ Mono-ion Oscillator Iii,”
Bulletin of the American Physical Society 20, 637 (1975).
[7] T.W. Hnsch and A.L. Schawlow, “Cooling of gases by laser radiation,” Optics
Communications 13, 68 (1975).
[8] A. Ashkin, “Trapping of Atoms by Resonance Radiation Pressure,” Physical
Review Letters 40, 729 (1978).
[9] J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Physical
Review A 21, 1606 (1980).
[10] Steven Chu, “Nobel Lecture: The manipulation of neutral particles,” Reviews
of Modern Physics 70, 685 (1998).
[11] Claude N. Cohen-Tannoudji, “Nobel Lecture: Manipulating atoms with
photons,” Reviews of Modern Physics 70, 707 (1998).
[12] William D. Phillips, “Nobel Lecture: Laser cooling and trapping of neutral
atoms,” Reviews of Modern Physics 70, 721 (1998).
168
[13] M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A.
Cornell, “Observation of Bose-Einstein Condensation in a Dilute Atomic
Vapor,” Science 269, 198 (1995).
[14] K. B. Davis, M. O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee,
D. M. Kurn, and W. Ketterle, “Bose-Einstein Condensation in a Gas of Sodium
Atoms,” Physical Review Letters 75, 3969 (1995).
[15] C. C. Bradley, C. A. Sackett, J. J. Tollett, and R. G. Hulet, “Evidence of
Bose-Einstein Condensation in an Atomic Gas with Attractive Interactions,”
Physical Review Letters 75, 1687 (1995).
[16] Paul D. Lett, Richard N. Watts, Christoph I. Westbrook, William D. Phillips,
Phillip L. Gould, and Harold J. Metcalf, “Observation of Atoms Laser Cooled
below the Doppler Limit,” Physical Review Letters 61, 169 (1988).
[17] J. Dalibard and C. Cohen-Tannoudji, “Laser cooling below the Doppler limit
by polarization gradients: simple theoretical models,” Journal of the Optical
Society of America B 6, 2023 (1989).
[18] A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji,
“Laser Cooling below the One-Photon Recoil Energy by Velocity-Selective
Coherent Population Trapping,” Physical Review Letters 61, 826 (1988).
[19] Mark Kasevich and Steven Chu, “Laser cooling below a photon recoil with
three-level atoms,” Physical Review Letters 69, 1741 (1992).
[20] J. Lawall, S. Kulin, B. Saubamea, N. Bigelow, M. Leduc, and C. Cohen-
Tannoudji, “Three-Dimensional Laser Cooling of Helium Beyond the Single-
Photon Recoil Limit,” Physical Review Letters 75, 4194 (1995).
[21] D. W. Keith, M. L. Schattenburg, Henry I. Smith, and D. E. Pritchard,
“Diffraction of Atoms by a Transmission Grating,” Physical Review Letters
61, 1580 (1988).
[22] O. Carnal, M. Sigel, T. Sleator, H. Takuma, and J. Mlynek, “Imaging and
focusing of atoms by a fresnel zone plate,” Physical Review Letters 67, 3231
(1991).
[23] T. Sleator, T. Pfau, V. Balykin, and J. Mlynek, “Imaging and focusing of
an atomic beam with a large period standing light wave,” Applied Physics B:
Lasers and Optics 54, 375 (1992). 10.1007/BF00325383.
[24] Philip E. Moskowitz, Phillip L. Gould, Susan R. Atlas, and David E. Pritchard,
“Diffraction of an Atomic Beam by Standing-Wave Radiation,” Physical Review
Letters 51, 370 (1983).
169
[25] T. Pfau, Ch. Kurtsiefer, C. S. Adams, M. Sigel, and J. Mlynek, “Magneto-
optical beam splitter for atoms,” Physical Review Letters 71, 3427 (1993).
[26] O. Carnal and J. Mlynek, “Young’s double-slit experiment with atoms: A simple
atom interferometer,” Physical Review Letters 66, 2689 (1991).
[27] David W. Keith, Christopher R. Ekstrom, Quentin A. Turchette, and David E.
Pritchard, “An interferometer for atoms,” Physical Review Letters 66, 2693
(1991).
[28] Ernst M. Rasel, Markus K. Oberthaler, Herman Batelaan, Jo¨rg Schmiedmayer,
and Anton Zeilinger, “Atom Wave Interferometry with Diffraction Gratings of
Light,” Physical Review Letters 75, 2633 (1995).
[29] David M. Giltner, Roger W. McGowan, and Siu Au Lee, “Atom Interferometer
Based on Bragg Scattering from Standing Light Waves,” Physical Review
Letters 75, 2638 (1995).
[30] G. Santarelli, Ph. Laurent, P. Lemonde, A. Clairon, A. G. Mann, S. Chang,
A. N. Luiten, and C. Salomon, “Quantum Projection Noise in an Atomic
Fountain: A High Stability Cesium Frequency Standard,” Physical Review
Letters 82, 4619 (1999).
[31] Masao Takamoto, Feng-Lei Hong, Ryoichi Higashi, and Hidetoshi Katori, “An
optical lattice clock,” Nature 435, 321 (2005).
[32] Maciej Lewenstein, Anna Sanpera, Veronica Ahufinger, Bogdan Damski, Aditi
Sen, and Ujjwal Sen, “Ultracold atomic gases in optical lattices: mimicking
condensed matter physics and beyond,” Advances in Physics 56, 243 (2007).
[33] B. DeMarco and D. S. Jin, “Onset of Fermi Degeneracy in a Trapped Atomic
Gas,” Science 285, 1703 (1999).
[34] M. Greiner, C. A. Regal, and D. S. Jin, “Emergence of a molecular Bose-Einstein
condensate from a Fermi gas,” Nature 426, 537 (2003).
[35] C. Monroe, “Quantum information processing with atoms and photons,” Nature
416, 238 (2002).
[36] H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer,
1999).
[37] D. A. Steck, “Quantum and Atom Optics,” course notes available online at
http://steck.us/teaching (2006).
170
[38] L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover
Publications, 1987).
[39] Marlan O. Scully and M. Suhail Zubairy, Quantum Optics (Cambridge
University Press, 2002).
[40] P. D. Lett, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, and C. I.
Westbrook, “Optical Molasses,” Journal of the Optical Society of America B 6,
2084 (1989).
[41] D. J. Wineland and W. M. Itano, “Laser cooling,” Physics Today 40, 34 (1987).
[42] John S. Townsend, A Modern Approach to Quantum Mechanics (University
Science Books, 2000).
[43] E. L. Raab, M. Prentiss, Alex Cable, Steven Chu, and D. E. Pritchard,
“Trapping of Neutral Sodium Atoms with Radiation Pressure,” Physical Review
Letters 59, 2631 (1987).
[44] C. S. Adams and E. Riis, “Laser cooling and trapping of neutral atoms,”
Progress in Quantum Electronics 21, 1 (1997).
[45] Steven Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental
Observation of Optically Trapped Atoms,” Physical Review Letters 57, 314
(1986).
[46] Steven L. Rolston, Christoph Gerz, Kristian Helmerson, P. S. Jessen, Paul D.
Lett, William D. Phillips, R. J. Spreeuw, and C. I. Westbrook, “Trapping
atoms with optical potentials,” in 1992 Shanghai International Symposium on
Quantum Optics, vol. 1726, p. 205 (SPIE, 1992).
[47] Rudolf Grimm, Matthias Weidemller, and Yurii B. Ovchinnikov, “Optical
Dipole Traps for Neutral Atoms,” in Advances In Atomic, Molecular, and
Optical Physics, Benjamin Bederson and Herbert Walther, Eds., vol. 42, p. 95
(Academic Press, 2000).
[48] C. J. Myatt, N. R. Newbury, R. W. Ghrist, S. Loutzenhiser, and C. E. Wieman,
“Multiply loaded magneto-optical trap,” Optics Letters 21, 290 (1996).
[49] K. I. Lee, J. A. Kim, H. R. Noh, and W. Jhe, “Single-beam atom trap in a
pyramidal and conical hollow mirror,” Optics Letters 21, 1177–1179 (1996).
[50] J. A. Kim, K. I. Lee, H. R. Noh, and W. Jhe, “Atom trap in an axicon mirror,”
Optics Letters 22 (1997).
171
[51] Carl E. Wieman and Leo Hollberg, “Using diode lasers for atomic physics,”
Review of Scientific Instruments 62, 1 (1991).
[52] J. C. Camparo, “The diode laser in atomic physics,” Contemporary Physics 26,
443 (1985).
[53] Amnon Yariv, Optical Electronics in Modern Communications (Oxford
University Press, 1997).
[54] K. B. MacAdam, A. Steinbach, and C. Wieman, “A narrow-band tunable diode
laser system with grating feedback, and a saturated absorption spectrometer for
Cs and Rb,” American Journal of Physics 60, 1098 (1992).
[55] D. A. Steck, Quantum Chaos, Transport, and Decoherence in Atom Optics,
Ph.D. thesis, University of Texas, Austin, Texas (2001).
[56] B. G. Klappauf, Experimental Studes of Quantum Chaos with Trapped Cesium,
Ph.D. thesis, University of Texas, Austin, Texas (1998).
[57] W. H. Oskay, Atom Optics Experiments in Quantum Chaos, Ph.D. thesis,
University of Texas, Austin, Texas (2001).
[58] T. Li, Manipulation of Cold Atoms Using an Optical One-Way Barrier, Ph.D.
thesis, University of Oregon, Eugene, Oregon (2008).
[59] Patrick McNicholl and Harold J. Metcalf, “Synchronous cavity mode and
feedback wavelength scanning in dye laser oscillators with gratings,” Applied
Optics 24, 2757 (1985).
[60] M. de Labachelerie and G. Passedat, “Mode-hop suppression of Littrow grating-
tuned lasers,” Applied Optics 32, 269 (1993).
[61] M. de Labachelerie, H. Sasada, and G. Passedat, “Mode-hop suppression of
Littrow grating-tuned lasers: erratum,” Applied Optics 33, 3817 (1994).
[62] Conoptics Inc., “Product Notes, Optical Isolators,”
http://www.conoptics.com/Optical-Isolators-Products.html.
[63] P. G. Pappas, M. M. Burns, D. D. Hinshelwood, M. S. Feld, and D. E.
Murnick, “Saturation spectroscopy with laser optical pumping in atomic
barium,” Physical Review A 21, 1955 (1980).
[64] D. W. Preston, “Doppler-free saturated absorption: Laser spectroscopy,”
American Journal of Physics 64, 1432 (1996).
[65] G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency
modulation (FM) spectroscopy,” Applied Physics B 32, 145 (1983).
172
[66] J. J. Arlt, O. Marag, S. Webster, S. Hopkins, and C. J. Foot, “A pyramidal
magneto-optical trap as a source of slow atoms,” Optics Communications 157,
303 (1998).
[67] A. Camposeo, A. Piombini, F. Cervelli, F. Tantussi, F. Fuso, and E. Arimondo,
“A cold cesium atomic beam produced out of a pyramidal funnel,” Optics
Communications 200, 231 (2001).
[68] James M. Kohel, Jaime Ramirez-Serrano, Robert J. Thompson, Lute Maleki,
Joshua L. Bliss, and Kenneth G. Libbrecht, “Generation of an intense cold-atom
beam from a pyramidal magneto-optical trap: experiment and simulation,”
Journal of the Optical Society of America B 20, 1161 (2003).
[69] Rob Williamson, P. Voytas, R. Newell, and Thad Walker, “A magneto-optical
trap loaded from a pyramidal funnel,” Optics Express 3, 111 (1998).
[70] SG Cox, PF Griffin, CS Adams, D DeMille, and E Riis, “Reusable ultrahigh
vacuum viewport bakeable to 240◦C,” Review of Scientific Instruments 74, 3185
(2003).
[71] K. M. Birnbaum and The Quantum Optics Group,
“Ultra-High Vacuum Chambers,” (2005). URL
http://www.its.caltech.edu/∼qoptics/Vacuum/UHV chambers.pdf.
[72] Y. T. Sasaki, “A survey of vacuum material cleaning procedures: A
subcommittee report of the American Vacuum Society Recommended Practices
Committee,” Journal of Vacuum Science & Technology A 9, 2025 (1991).
[73] A. Mosk, Tutorial on Experimental Physics of Ultracold Gases (Wiley-VCH
Verlag GmbH & Co. KGaA, 2005).
[74] M. Bernardini, S. Braccini, R. De Salvo, A. Di Virgilio, A. Gaddi, A. Gennai,
G. Genuini, A. Giazotto, G. Losurdo, H. B. Pan, A. Pasqualetti, D. Passuello,
P. Popolizio, F. Raffaelli, G. Torelli, Z. Zhang, C. Bradaschia, R. Del Fabbro,
I. Ferrante, F. Fidecaro, P. La Penna, S. Mancini, R. Poggiani, P. Narducci,
A. Solina, and R. Valentini, “Air bake-out to reduce hydrogen outgassing from
stainless steel,” Journal of Vacuum Science & Technology A 16, 188 (1998).
[75] J. F. O’Hanlon, A User’s Guide to Vacuum Technology (John Wiley & Sons,
Inc., 2003).
[76] M. Fuchs, Development of a High Power Stabilized Diode Laser System,
Master’s thesis, University of Oregon, Eugene, Oregon (2006).
173
[77] Peter E. Gaskell, Jeremy J. Thorn, Sequoia Alba, and Daniel A. Steck, “An
open-source, extensible system for laboratory timing and control,” Review of
Scientific Instruments 80, 115103 (2009).
[78] Jeremy J. Thorn, Elizabeth A. Schoene, Tao Li, and Daniel A. Steck, “Dynamics
of cold atoms crossing a one-way barrier,” Physical Review A 79, 063402 (2009).
[79] M. G. Raizen, A. M. Dudarev, Qian Niu, and N. J. Fisch, “Compression of
Atomic Phase Space Using an Asymmetric One-Way Barrier,” Physical Review
Letters 94, 053003 (2005).
[80] A. Ruschhaupt and J. G. Muga, “Atom diode: A laser device for a unidirectional
transmission of ground-state atoms,” Physical Review A 70, 061604(R) (2004).
[81] A. M. Dudarev, M. Marder, Q. Niu, N. J. Fisch, and M. G. Raizen, “Statistical
mechanics of an optical phase space compressor,” Europhysics Letters 70, 761
(2005).
[82] Sang Wook Kim and Mahn-Soo Choi, “Decoherence-Driven Quantum
Transport,” Physical Review Letters 95, 226802 (2005).
[83] A. Ruschhaupt and J. G. Muga, “Adiabatic interpretation of a two-level atom
diode, a laser device for unidirectional transmission of ground-state atoms,”
Physical Review A 73, 013608 (2006).
[84] A. Ruschhaupt, J. G. Muga, and M. G. Raizen, “Improvement by laser
quenching of an ‘atom diode’: a one-way barrier for ultra-cold atoms,” Journal
of Physics B: Atomic, Molecular and Optical Physics 39, L133 (2006).
[85] A. Ruschhaupt, J. G. Muga, and M. G. Raizen, “One-photon atomic cooling
with an optical Maxwell demon valve,” Journal of Physics B: Atomic, Molecular
and Optical Physics 39, 3833 (2006).
[86] G. N. Price, S. T. Bannerman, E. Narevicius, and M. G. Raizen, “Single-photon
atomic cooling,” Laser Physics 17, 965 (2007).
[87] A. Ruschhaupt and J. G. Muga, “Three-dimensional effects in atom diodes:
Atom-optical devices for one-way motion,” Physical Review A 76, 013619
(2007).
[88] A. Ruschhaupt and J. G. Muga, “Control of atomic motion with an atom-
optical diode on a ring,” Journal of Physics B: Atomic, Molecular and Optical
Physics 41, 205503 (2008).
[89] G. N. Price, S. T. Bannerman, K. Viering, E. Narevicius, and M. G. Raizen,
“Single-Photon Atomic Cooling,” Physical Review Letters 100, 093004 (2008).
174
[90] J. J. Thorn, E. A. Schoene, T. Li, and D. A. Steck, “Experimental Realization
of an Optical One-Way Barrier for Neutral Atoms,” Physical Review Letters
100, 240407 (2008).
[91] Ron Folman, Peter Kru¨ger, Donatella Cassettari, Bjo¨rn Hessmo, Thomas
Maier, and Jo¨rg Schmiedmayer, “Controlling Cold Atoms using Nanofabricated
Surfaces: Atom Chips,” Physical Review Letters 84, 4749 (2000).
[92] R. Folman, P. Kru¨ger, J. Schmiedmayer, J. Denschlag, and C. Henkel,
“Microscopic Atom Optics: From Wires to an Atom Chip,” Advances in Atomic,
Molecular, and Optical Physics 48, 263 (2002).
[93] J. C. Maxwell, Theory of Heat (Longmans, Green, and Co., New York, 1871).
[94] Charles H. Bennett, “Demons, Engines and the Second Law,” Scientific
American 257, 108 (1987).
[95] R. J. Scully and M. O. Scully, The Demon and the Quantum (Wiley-VCH,
Weinheim, 2007).
[96] Kilian Singer, Selim Jochim, Marcel Mudrich, Allard Mosk, and Matthias
Weidemuller, “Low-cost mechanical shutter for light beams,” Review of
Scientific Instruments 73, 4402 (2002).
[97] J. Dalibard and C. Cohen-Tannoudji, “Laser cooling below the Doppler limit
by polarization gradients: simple theoretical models,” Journal of the Optical
Society of America B 6, 2023 (1989).
[98] S. J. M. Kuppens, K. L. Corwin, K. W. Miller, T. E. Chupp, and C. E. Wieman,
“Loading an optical dipole trap,” Physical Review A 62, 013406 (2000).
[99] P. S. Julienne and Jacques Vigue´, “Cold collisions of ground- and excited-state
alkali-metal atoms,” Physical Review A 44, 4464 (1991).
[100] P. D. Lett, K. Mølmer, S. D. Gensemer, K. Y. N. Tan, A. Kumarakrishnan,
C. D. Wallace, and P. L. Gould, “Hyperfine structure modifications of collisional
losses from light-force atom traps,” Journal of Physics B: Atomic, Molecular
and Optical Physics 28, 65 (1995).
[101] J. D. Miller, R. A. Cline, and D. J. Heinzen, “Photoassociation spectrum of
ultracold Rb atoms,” Physical Review Letters 71, 2204 (1993).
[102] Alan Gallagher and David E. Pritchard, “Exoergic collisions of cold Na∗-Na,”
Physical Review Letters 63, 957 (1989).
175
[103] Elizabeth A. Schoene, Jeremy J. Thorn, and Daniel A. Steck, “Cooling atoms
with a moving one-way barrier,” Physical Review A 82, 023419 (2010).
[104] T. Kuwamoto, K. Honda, Y. Takahashi, and T. Yabuzaki, “Magneto-optical
trapping of Yb atoms using an intercombination transition,” Physical Review
A 60, R745 (1999).
[105] C. C. Bradley, J. J. McClelland, W. R. Anderson, and R. J. Celotta, “Magneto-
optical trapping of chromium atoms,” Physical Review A 61, 053407 (2000).
[106] J. J. McClelland and J. L. Hanssen, “Laser Cooling without Repumping: A
Magneto-Optical Trap for Erbium Atoms,” Physical Review Letters 96, 143005
(2006).
[107] K.-A. Brickman, M.-S. Chang, M. Acton, A. Chew, D. Matsukevich, P. C.
Haljan, V. S. Bagnato, and C. Monroe, “Magneto-optical trapping of
cadmium,” Physical Review A 76, 043411 (2007).
[108] H. Hachisu, K. Miyagishi, S. G. Porsev, A. Derevianko, V. D. Ovsiannikov,
V. G. Pal’chikov, M. Takamoto, and H. Katori, “Trapping of Neutral Mercury
Atoms and Prospects for Optical Lattice Clocks,” Physical Review Letters 100,
053001 (2008).
[109] Mingwu Lu, Seo Ho Youn, and Benjamin L. Lev, “Trapping Ultracold
Dysprosium: A Highly Magnetic Gas for Dipolar Physics,” Physical Review
Letters 104, 063001 (2010).
[110] E. Narevicius, S. T. Bannerman, and M. G. Raizen, “Single-photon molecular
cooling,” New Journal of Physics 11, 055046 (2009).
[111] S. T. Bannerman, G. N. Price, K. Viering, and M. G. Raizen, “Single-
photon cooling at the limit of trap dynamics: Maxwell’s demon near maximum
efficiency,” New Journal of Physics 11, 063044 (2009).
[112] S. Balik, A. L. Win, and M. D. Havey, “Imaging-based parametric resonance in
an optical dipole-atom trap,” Physical Review A 80, 023404 (2009).
[113] T. A. Savard, K. M. O’Hara, and J. E. Thomas, “Laser-noise-induced heating
in far-off resonance optical traps,” Physical Review A 56, R1095 (1997).
[114] Charles S. Adams, Heun Jin Lee, Nir Davidson, Mark Kasevich, and Steven
Chu, “Evaporative Cooling in a Crossed Dipole Trap,” Physical Review Letters
74, 3577 (1995).
[115] H. J. Lee, C. S. Adams, M. Kasevich, and S. Chu, “Raman Cooling of Atoms
in an Optical Dipole Trap,” Physical Review Letters 76, 2658 (1996).
176
[116] M. Zielonkowski, I. Manek, U. Moslener, P. Rosenbusch, and R. Grimm,
“Manipulation of spin-polarized atoms in an optical dipole-force trap,”
Europhysics Letters 44, 700 (1998).
[117] Vladan Vuletic´, Cheng Chin, Andrew J. Kerman, and Steven Chu, “Degenerate
Raman Sideband Cooling of Trapped Cesium Atoms at Very High Atomic
Densities,” Physical Review Letters 81, 5768 (1998).