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arXiv:1705.10383 · Physical Review A

Coherent properties of a tunable low-energy electron-matter-wave source

A. Pooch, Michael Seidling, Nicole Kerker, Robin Röpke, A. Rembold, Wei‐Chung Chang, Ing‐Shouh Hwang, Alexander Stibor

Published Jan 12, 2018• 13 citations
arXivHTMLPDF

Abstract

A general challenge in various quantum experiments and applications is to develop suitable sources for coherent particles. In particular, recent progress in microscopy, interferometry, metrology, decoherence measurements, and chip-based applications rely on intensive, tunable, coherent sources for free low-energy electron-matter waves. In most cases, the electrons get field emitted from a metal nanotip, where its radius and geometry toward a counter electrode determines the field distribution and the emission voltage. A higher emission is often connected to faster electrons with smaller de Broglie wavelengths, requiring larger pattern magnification after matter-wave diffraction or interferometry. This can be prevented with a well-known setup consisting of two counter electrodes that allow independent setting of the beam intensity and velocity. However, it needs to be tested if the coherent properties of such a source are preserved after the acceleration and deceleration of the electrons. Here, we study the coherence of the beam in a biprism interferometer with a single atom tip electron field emitter if the particle velocity and wavelength varies after emission. With a Wien filter measurement and a contrast correlation analysis we demonstrate that the intensity of the source at a certain particle wavelength can be enhanced up to a factor of 6.4 without changing the transverse and longitudinal coherence of the electron beam. In addition, the energy width of the single atom tip emitter was measured to be 377 meV, corresponding to a longitudinal coherence length of 82 nm. The design has potential applications in interferometry, microscopy, and sensor technology.

DOI
10.1103/physreva.97.013611

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A general challenge in various quantum experiments and applications is to develop suitable sources for coherent particles. In particular, recent progress in microscopy, interferometry, metrology, decoherence measurements, and chip-based applications rely on intensive, tunable, coherent sources for free low-energy electron-matter waves. In most cases, the electrons get field emitted from a metal nanotip, where its radius and geometry toward a counter electrode determines the field distribution and the emission voltage. A higher emission is often connected to faster electrons with smaller de Broglie wavelengths, requiring larger pattern magnification after matter-wave diffraction or interferometry. This can be prevented with a well-known setup consisting of two counter electrodes that allow independent setting of the beam intensity and velocity. However, it needs to be tested if the coherent properties of such a source are preserved after the acceleration and deceleration of the electrons. Here, we study the coherence of the beam in a biprism interferometer with a single atom tip electron field emitter if the particle velocity and wavelength varies after emission. With a Wien filter measurement and a contrast correlation analysis we demonstrate that the intensity of the source at a certain particle wavelength can be enhanced up to a factor of 6.4 without changing the transverse and longitudinal coherence of the electron beam. In addition, the energy width of the single atom tip emitter was measured to be 377 meV, corresponding to a longitudinal coherence length of 82 nm. The design has potential applications in interferometry, microscopy, and sensor technology.
A general challenge in various quantum experiments and applications is to develop suitable sources for coherent particles. In particular, recent progress in microscopy, interferometry, metrology, decoherence measurements and chip based applications rely on intensive, tunable, coherent sources for free low energy electron matter waves. In most cases, the electrons get field emitted from a metal nanotip where its radius and geometry towards a counter electrode determines the field distribution and the emission voltage. A higher emission is often connected to faster electrons with smaller de Broglie wavelengths, requiring larger pattern magnification after matter wave diffraction or interferometry. This can be prevented with a well-known setup consisting of two counter electrodes that allow independent setting of the beam intensity and velocity. However, it needs to be tested if the coherent properties of such a source are preserved after the acceleration and deceleration of the electrons. Here, we study the coherence of the beam in a biprism interferometer with a single atom tip electron field emitter if the particle velocity and wavelength varies after emission. With a Wien filter measurement and a contrast correlation analysis we demonstrate that the intensity of the source at a certain particle wavelength can be enhanced up to a factor of 33 without changing the transverse and longitudinal coherence of the electron beam. In addition, the energy width of the single atom tip emitter was measured to be 377 meV, corresponding to a longitudinal coherence length of 82 nm. The design has potential applications in interferometry, microscopy and sensor technology
Remarkable progress can be observed in recent years in the controlled emission, guiding, and detection of coherent, free electrons. Those methods were applied in matter wave interferometers leading to high phase sensitivities and precise sensor technologies for dephasing influences such as mechanical vibrations or electromagnetic frequencies. However, the previous devices have been large laboratory setups. For future sensor applications or tests of the coherence properties of an electron source, small, portable interferometers are required. Here, we demonstrate a compact biprism electron interferometer that can be used for mobile applications. The design was optimized for small dimensions by beam path simulations. The interferometer has a length between the tip and the superposition plane before magnification of only 47 mm and provides electron interference patterns with a contrast up to 42.7%. The detection of two dephasing frequencies at 50 and 150 Hz was demonstrated applying second order correlation and Fourier analysis of the interference data.
Electrons emitted from single-atom tips are analysed in a model with the tip as a round tubelike constriction. The source creates two-dimensional minimum wavepackets whose temporal evolution agrees well with observed beam divergences. With few-atom tips interference effects may arise due to the electron's non localized emission from several atoms. The phase space density of emitted electrons is around 10 −2 h −3 , and electron-electron correlation experiments become feasible. In ion field emission mode observed beam divergences are dominated by thermal broadening and other effects rather than quantum mechanical principles. Applications include electron interferometers of lower energy and wider beam separation than hitherto in use, as well as proton and possibly other ion interferometers. Highly focused low energy beams could also be produced.
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.
Longitudinal coherence in two-beam interferometers means that the two partial wave packets arrive in the plane of interference simultaneously. In charged-particle interferometers, this simultaneity can be lost due to a difference in the geometrical path lengths, a difference in the optical path length, or a difference in the group velocities for the two wave packets on parts of or all of the beam paths. Several of those influences can combine to yield a net relative spatial delay between the wave packets in the interference plane, thus causing a reduction of the interference fringe contrast. A Wien filter can be used in charged-matter-wave interferometry to compensate for this relative delay and thus to reestablish longitudinal coherence. A Wien filter consists of an electric and a magnetic field perpendicular both to each other and the beam path. In its matched state, i.e., when the electrostatic and the magnetic forces on the electrons exactly cancel each other, the Wien filter neither deflects the beams nor exerts any phase shift on the wave packets. However, wave packets traveling through the Wien filter on laterally separated paths propagate in regions of different electric potentials and in turn with different group velocities, which leads to a longitudinal shift of the wave packets relative to each other. Maximum longitudinal coherence (and thereby fringe contrast) can be restored by choosing the compensating delay caused by the Wien filter exactly opposite to the net relative delay caused by the influences mentioned.An experiment is presented that demonstrates this property of a Wien filter. The coherence-reviving action of a Wien filter is discussed in the context of the incoherent superposition in the registration plane of the plane waves corresponding to different wavelengths in the electron spectrum. It demonstrates that the quantum-mechanical coherence of the self-interacting plane-wave components of the wave packets describing the particle ensemble is more robust than the experimental loss of interference-fringe contrast often suggests. The availability of such a contrast-restoring device is especially important for very-low-energy (a few keV or less) electron interferometry. It is also likely to become important for future ion-beam interferometers.
We discuss recent advances towards matter-wave interference experiments with free beams of metallic and dielectric nanoparticles. They require a brilliant source, an efficient detection scheme and a coherent method to divide the de Broglie waves associated with these clusters: We describe an approach based on a magnetron sputtering source which ejects an intense cluster beam with a wide mass dispersion but a small velocity spread of Δv/v < 10%. The source is universal as it can be used with all conducting and many semiconducting or even insulating materials. Here we focus on metals and dielectrics with a low work function of the bulk and thus a low cluster ionization energy. This allows us to realize photoionization gratings as coherent matter-wave beam splitters and also to realize an efficient ionization detection scheme. These new methods are now combined in an upgraded Talbot-Lau interferometer with three 266 nm depletion gratings. We here describe the experimental boundary conditions and how to realize them in the lab. This next generation of near-field interferometers shall allow us to soon push the limits of matter-wave interference to masses up to 106 amu.