Electron orbital angular momentum: preparation, application and measurement
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The electron microscope is an ideal tool to prepare an electron into a specified quantum state, entangle that state with states in a specimen of interest, and measure the electron final state to indirectly gain information about the specimen. There currently exist excellent technologies to prepare both momentum eigenstates (transmission electron microscopy) and position eigenstates (scanning transmission electron microscopy) in a narrow band of energy eigenstates. Similarly, measurement of the momentum and position final states is straightforward with post-specimen lenses and pixelated detectors. Measurement of final energy eigenstates is possible with magnetic electron energy loss spectrometers. In 2010 and 2011, several groups independently showed that it was straightforward to prepare electrons into orbital angular momentum eigenstates. This disseratation represents my contributions to the toolset we have to control these eigenstates: preparation, application (interaction with specimen states), and measurement. My collaborators and I showed that phase diffraction gratings efficiently produce electron orbital angular momentum eigenstates; that control of orbital angular momentum can be used to probe chirality and local magnetic fields; and that there are several routes toward efficient measurement.