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Advances in imaging and electron physics

Partially coherent quantum degenerate electron matter waves

Sam Keramati, Eric Jones, J. R. Armstrong, Herman Batelaan

Published Dec 18, 2019• 7 citations
Publisher
DOI
10.1016/bs.aiep.2019.11.002

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The use of electron beams is ubiquitous; electron microscopy, scanning tunneling microscopy, electron lithography, and electron diffractometry all use well-collimated and focused beams. On the other hand, quantum degenerate electron beams do currently not exist. The realization of such beams may impact all electron beam technologies and are interesting to pursue. Past attempts to reach degeneracy were hampered by the low degeneracy of continuously emitting electron sources. With the recent advent of ultra-short electron pulses, high degeneracy is expected. Coulomb repulsion and low quantum coherence are hurdles that need to be overcome. A quantum analysis of the electron degeneracy for partially coherent pulsed electron sources is presented. Two-particle coincidence spectra are obtained for source parameters that are currently available. The conclusive demonstration of the fermionic Hanbury-Brown Twiss (HBT) effect for free electrons is shown to be within reach, and our results support the claim that femto-second nanotip electron sources, both polarized and unpolarized, can manifest partial to complete quantum degeneracy with appreciable signal-to-noise-ratios for free electron pulses notwithstanding their small particle numbers.
We employ ptychography, a phase-retrieval imaging technique, to show experimentally that a partially coherent high-energy matter (electron) wave emanating from an extended source can be decomposed into a set of mutually independent modes of minimal rank. Partial coherence significantly determines the optical transfer properties of an electron microscope and so there has been much work on this subject. However, previous studies have employed forms of interferometry to determine spatial coherence between discrete points in the wave field. Here we use the density matrix to derive a formal quantum mechanical description of electron ptychography and use it to measure a full description of the spatial coherence of a propagating matter wave field, at least within the fundamental uncertainties of the measurements we can obtain.