Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Wien filter: A wave-packet-shifting device for restoring longitudinal coherence in charged-matter-wave interferometers

Marc C. Nicklaus, FRANZ HASSELBACH

Published Jul 1, 1993• 57 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.48.152

Related papers

Interferometric (Fourier-Spectroscopic) Measurement of Electron Energy Distributions

FRANZ HASSELBACH, A. Schäfer

Möllenstedt and Wohland proposed in 1980 two methods for measuring the coherence lengths of electron wave packets interferometrically by observing interference fringe contrast in dependence on the longitudinal shift of the wave packets. In both cases an electron beam is split by an electron optical biprism into two coherent wave packets, and subsequently both packets travel part of their way to the interference plane in regions of different electric potential, either in a Faraday cage (Fig. 1a) or in a Wien filter (crossed electric and magnetic fields, Fig. 1b). In the Faraday cage the phase and group velocity of the upper beam (Fig.1a) is retarded or accelerated according to the cage potential. In the Wien filter the group velocity of both beams varies with its excitation while the phase velocity remains unchanged. The phase of the electron wave is not affected at all in the compensated state of the Wien filter since the electron optical index of refraction in this state equals 1 inside and outside of the Wien filter.

Proceedings annual meeting Electron Microscopy Society of America•Aug 12, 1990•5 citations

Coherence and spectral filtering in neutron interferometry

Helmut Kaiser, R. Clothier, S. A. Werner +2 more

The coherence length of a neutron wave packet depends on the spectral width of the distribution of wave vectors that make up the packet. The coherent overlap of the wave packets traversing the two beam paths in a perfect-silicon-crystal neutron interferometer (NI) is altered by placing a material with a neutron-nuclear optical potential in one of the beam paths in the NI. If the optical potential is positive, it causes a delay of the wave packet and a loss of fringe visibility. By use of an analyzer crystal, we narrow the spectral distribution after the mixing and interference has occurred in the last crystal slab of the NI. This increases the coherence length and restores some of the fringe visibility.

Physical Review A•Jan 1, 1992•65 citations

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

A. Pooch, Michael Seidling, Nicole Kerker +5 more

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.

arXiv:1705.10383•Physical Review A•Jan 12, 2018•13 citations

Intensity amplification for a coherent low energy electron matter wave source

A. Pooch, Michael Seidling, Nicole Kerker +5 more

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

•May 29, 2017•0 citations

Restoration of neutron interferometer contrast by post-interference filtering

J. W. G. Wignall

It is argued that the results of a recent neutron interference experiment [Kaiser et al., Phys. Rev. A 45, 31 (1992)], in which contrast lost as a result of difference in effective path lengths is restored by wavelength filtering after recombination, cannot be construed as evidence against the notion that a neutron is a physically real wave packet.

Physical Review A•Feb 1, 1993•1 citation

Coherence and Decoherence

Helmut Rauch, Samuel A. Werner

Abstract This chapter describes a rather broad selection of neutron interferometry experiments whose theoretical description requires an understanding of the mutual coherence function, and the sensitive experimental techniques utilized. Within the interferometer the coherent beams can be influenced by interactions with fields and material media in space and time causing phase shifts and wave packet delays that substantially affect the outgoing beams. Post-selection experiments involving spectral filtering and time-of-flight analysis are described. The phase-echo effect is described; it is a generalization of the spin-echo effect. Placing statistical or deterministic absorbers within the interferometer affects the outgoing coherence properties of beams quite differently. Low counting rate interference experiments show time pair-correlation effects characteristic of Poissonian statistical beams. Decoherence effects are investigated to study the transition from a quantum to a classical regime.

Oxford University Press eBooks•Jan 15, 2015•0 citations
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.
Möllenstedt and Wohland proposed in 1980 two methods for measuring the coherence lengths of electron wave packets interferometrically by observing interference fringe contrast in dependence on the longitudinal shift of the wave packets. In both cases an electron beam is split by an electron optical biprism into two coherent wave packets, and subsequently both packets travel part of their way to the interference plane in regions of different electric potential, either in a Faraday cage (Fig. 1a) or in a Wien filter (crossed electric and magnetic fields, Fig. 1b). In the Faraday cage the phase and group velocity of the upper beam (Fig.1a) is retarded or accelerated according to the cage potential. In the Wien filter the group velocity of both beams varies with its excitation while the phase velocity remains unchanged. The phase of the electron wave is not affected at all in the compensated state of the Wien filter since the electron optical index of refraction in this state equals 1 inside and outside of the Wien filter.
The coherence length of a neutron wave packet depends on the spectral width of the distribution of wave vectors that make up the packet. The coherent overlap of the wave packets traversing the two beam paths in a perfect-silicon-crystal neutron interferometer (NI) is altered by placing a material with a neutron-nuclear optical potential in one of the beam paths in the NI. If the optical potential is positive, it causes a delay of the wave packet and a loss of fringe visibility. By use of an analyzer crystal, we narrow the spectral distribution after the mixing and interference has occurred in the last crystal slab of the NI. This increases the coherence length and restores some of the fringe visibility.
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
Abstract This chapter describes a rather broad selection of neutron interferometry experiments whose theoretical description requires an understanding of the mutual coherence function, and the sensitive experimental techniques utilized. Within the interferometer the coherent beams can be influenced by interactions with fields and material media in space and time causing phase shifts and wave packet delays that substantially affect the outgoing beams. Post-selection experiments involving spectral filtering and time-of-flight analysis are described. The phase-echo effect is described; it is a generalization of the spin-echo effect. Placing statistical or deterministic absorbers within the interferometer affects the outgoing coherence properties of beams quite differently. Low counting rate interference experiments show time pair-correlation effects characteristic of Poissonian statistical beams. Decoherence effects are investigated to study the transition from a quantum to a classical regime.