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

arXiv:physics/0609063 · Physical Review A

Electron interferometry with nanogratings

Alexander D. Cronin, Benjamin J. McMorran

Published Dec 26, 2006• 30 citations
arXivHTMLPDF

Abstract

We present an electron interferometer based on near-field diffraction from two nanostructure gratings. Lau fringes are observed with an imaging detector, and revivals in the fringe visibility occur as the separation between gratings is increased from $0.2\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}2.7\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$. The oscillations in visibility depend predictably on the wavelength of incident electrons. This verifies that $5\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ electrons diffracted by nanostructures remain coherent after propagating farther than the Talbot length, and hence proves that a Talbot-Lau interferometer for electrons can be built with nanostructure gratings. Distorted fringes due to a phase object are used to demonstrate an application for this type of electron interferometer.

DOI
10.1103/physreva.74.061602

Related papers

Electron matter optics and an electron Mach -Zehnder interferometer

Glen Gronniger

The diffraction of electrons by natural crystal structures was first observed in 1927. Before the start of this work, it was not clear whether or not the high quality gratings currently available could be used for electron diffraction due to image charge and other electron grating interactions. We observe for the first time electron diffraction from man made diffraction gratings of 100 nm periodicity. The high quality of diffraction and the ability to "pick" the periodicity allowed us to construct the first Mach-Zehnder electron interferometer using these gratings. Multiple approaches, including a prototype of our current interferometer and the combination of a grating with an electron bi-prism, were unsuccessful. Many stabilization issues must be overcome to observe electron interference fringes in the interferometer. Many experimental design ideas were used to reach proper stabilization requirements. The final interferometer design constructed was the only interferometer to obtain electron interference fringes. The theoretical model used to analyze the data is based on the path integral formalism. This calculates the amplitude associated with all classical paths through the experimental device. The sum of all amplitudes, the path integral, yields the resulting probability at the detection screen. We obtain good fits between our path integral calculations and experimental data. Alternate explanations of our data, such as the possibilities of Talbot Lau and classical Moiré interferometers are ruled out in favor of the Mach-Zehnder explanation. This type of interferometer could be used for future experiments. An experiment for which the fundamental quantum mechanical experiment has never been done; observing the dispersion-less nature of the Aharonov-Bohm Effect, may lend itself to the characteristics of this type of interferometer. Preliminary calculations have been performed to investigate the feasibility of using the grating technology to perform the required experiment.

•Jan 1, 2006•0 citations

Near-field diffraction of protons by a nanostructured metallic grating under external electric field: asymmetry and sidebands in Talbot self-imaging

Sushanta Barman, Sudeep Bhattacharjee

Abstract Self-imaging in near-field diffraction is a practical application of coherent manipulation of matter waves in Talbot interferometry. In this work, near-field diffraction of protons by a nanostructured metallic grating under the influence of (a) uniform, (b) spatially modulated, and (c) temporally modulated electric fields are investigated. Time-domain simulations of two-dimensional Gaussian wave packets for protons are performed by solving the time-dependent Schrödinger’s equation using the generalized finite difference time domain method for quantum systems. Effects of strength (E 0) and orientation (θ) of the uniform electric field on the diffraction properties, such as fringe pattern, intensity of the peaks, fringe shift, and visibility, are investigated. The results show that the Talbot fringes shift significantly in the transverse direction even for a small change in the applied electric field ( <?CDATA $\Delta E_0 = 0.1$?> Δ E 0 = 0.1 V m−1) and its orientation ( <?CDATA $\Delta \theta = 0.1^{\circ}$?> Δ θ = 0.1 ∘ ). Moreover, electric field-dependent fringe visibility is observed, which can be tuned by E 0 and θ. The potential barriers arising from a spatially modulated electric field are observed to cause significant distortions in the Talbot patterns when the modulation length ( <?CDATA $\lambda^{\prime}$?> λ ′ ) is equal to the de Broglie wavelength ( <?CDATA $\lambda_\mathrm{dB}$?> λ d B ). Sidebands are observed in the Talbot pattern due to the efficient transfer of energy from the oscillating field to the wave packet when the frequency of oscillation (ω) is of the order of ω 0 ( <?CDATA $ = 2\pi/T_0$?> = 2 π / T 0 ), where T 0 is the interaction time. This study will be helpful in uniform electric field-controlled precision metrology, developing a highly sensitive electric field sensor based on Talbot interference, and precisely aligning the matter wave optical setup. Furthermore, the sidebands in the Talbot fringe can be used as a precise tool for momentum splitter in matter wave interferometry.

arXiv:2304.10497•New Journal of Physics•Aug 1, 2023•2 citations

Model for partial coherence and wavefront curvature in grating interferometers

Benjamin J. McMorran, Alexander D. Cronin

We examine how partial coherence and wavefront curvature of beams affect interference fringes behind diffraction gratings. We simulate (1) the Talbot effect, (2) far-field diffraction, (3) Mach-Zehnader interferometers, (4) Talbot-Lau interferometers, and (5) Lau interferometers using a numerically efficient expression. We show how interference fringes in each case depend on the beam's initial width, its coherence width (transverse coherence length), and its wavefront curvature in directions both parallel and perpendicular to the grating bars. The separation between gratings and the rotational alignment of the gratings about the optical axis are also considered. The formula used for our simulations is derived using the mutual intensity function of a Gaussian Schell-model beam.

Physical Review A•Jul 1, 2008•29 citations

Matter-Wave Interferometer for Large Molecules

Björn Brezger, Lucia Hackermüller, S. Uttenthaler +3 more

We demonstrate a near-field Talbot-Lau interferometer for C70 fullerene molecules. Such interferometers are particularly suitable for larger masses. Using three free-standing gold gratings of 1 microm period and a transversally incoherent but velocity-selected molecular beam, we achieve an interference fringe visibility of 40% with high count rate. Both the high visibility and its velocity dependence are in good agreement with a quantum simulation that takes into account the van der Waals interaction of the molecules with the gratings and are in striking contrast to a classical moiré model.

arXiv:quant-ph/0202158•Physical Review Letters•Feb 26, 2002•333 citations

A charged particle Talbot-Lau interferometer and magnetic field sensing

Roger Bach, Glen Gronniger, Herman Batelaan

We present the first demonstration of a three grating Talbot-Lau interferometer for electrons. As a proof of principle, the interferometer is used to measure magnetic fields. The device is similar to the classical Moire deflectometer. The possibility to extend this work to build a scaled-up charged particle deflectometer or interferometer for sensitive magnetic field sensing is indicated.

arXiv:1305.7267•May 30, 2013•1 citation

Matter-wave interferometry with composite quantum objects

Markus Arndt, Nadine Dörre, Sandra Eibenberger +5 more

We discuss modern developments in quantum optics with organic molecules, clusters and nanoparticles -- in particular recent realizations of near-field matter-wave interferometry. A unified theoretical description in phase space allows us to describe quantum interferometry in position space and in the time domain on an equal footing. In order to establish matter-wave interferometers as a universal tool, which can accept and address a variety of nanoparticles, we elaborate on new quantum optical elements, such as diffraction gratings made of matter and light, as well as their absorptive and dispersive interaction with complex materials. We present Talbot-Lau interferometry (TLI), the Kapitza-Dirac-Talbot-Lau interferometer (KDTLI) and interferometry with pulsed optical gratings (OTIMA) as the most advanced devices to study the quantum wave nature of composite matter. These experiments define the current mass and complexity record in interferometric explorations of quantum macroscopicity and they open new avenues to quantum assisted metrology with applications in physical chemistry and biomolecular physics.

arXiv:1501.07770•Jan 30, 2015•10 citations
We present an electron interferometer based on near-field diffraction from two nanostructure gratings. Lau fringes are observed with an imaging detector, and revivals in the fringe visibility occur as the separation between gratings is increased from 0.2to2.7mm0.2\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}2.7\phantom{\rule{0.3em}{0ex}}\mathrm{mm}0.2to2.7mm. The oscillations in visibility depend predictably on the wavelength of incident electrons. This verifies that 5keV5\phantom{\rule{0.3em}{0ex}}\mathrm{keV}5keV electrons diffracted by nanostructures remain coherent after propagating farther than the Talbot length, and hence proves that a Talbot-Lau interferometer for electrons can be built with nanostructure gratings. Distorted fringes due to a phase object are used to demonstrate an application for this type of electron interferometer.
The diffraction of electrons by natural crystal structures was first observed in 1927. Before the start of this work, it was not clear whether or not the high quality gratings currently available could be used for electron diffraction due to image charge and other electron grating interactions. We observe for the first time electron diffraction from man made diffraction gratings of 100 nm periodicity. The high quality of diffraction and the ability to "pick" the periodicity allowed us to construct the first Mach-Zehnder electron interferometer using these gratings. Multiple approaches, including a prototype of our current interferometer and the combination of a grating with an electron bi-prism, were unsuccessful. Many stabilization issues must be overcome to observe electron interference fringes in the interferometer. Many experimental design ideas were used to reach proper stabilization requirements. The final interferometer design constructed was the only interferometer to obtain electron interference fringes. The theoretical model used to analyze the data is based on the path integral formalism. This calculates the amplitude associated with all classical paths through the experimental device. The sum of all amplitudes, the path integral, yields the resulting probability at the detection screen. We obtain good fits between our path integral calculations and experimental data. Alternate explanations of our data, such as the possibilities of Talbot Lau and classical Moiré interferometers are ruled out in favor of the Mach-Zehnder explanation. This type of interferometer could be used for future experiments. An experiment for which the fundamental quantum mechanical experiment has never been done; observing the dispersion-less nature of the Aharonov-Bohm Effect, may lend itself to the characteristics of this type of interferometer. Preliminary calculations have been performed to investigate the feasibility of using the grating technology to perform the required experiment.
Abstract Self-imaging in near-field diffraction is a practical application of coherent manipulation of matter waves in Talbot interferometry. In this work, near-field diffraction of protons by a nanostructured metallic grating under the influence of (a) uniform, (b) spatially modulated, and (c) temporally modulated electric fields are investigated. Time-domain simulations of two-dimensional Gaussian wave packets for protons are performed by solving the time-dependent Schrödinger’s equation using the generalized finite difference time domain method for quantum systems. Effects of strength (E 0) and orientation (θ) of the uniform electric field on the diffraction properties, such as fringe pattern, intensity of the peaks, fringe shift, and visibility, are investigated. The results show that the Talbot fringes shift significantly in the transverse direction even for a small change in the applied electric field ( <?CDATA ΔE0=0.1\Delta E_0 = 0.1ΔE0​=0.1?> Δ E 0 = 0.1 V m−1) and its orientation ( <?CDATA Δθ=0.1∘\Delta \theta = 0.1^{\circ}Δθ=0.1∘?> Δ θ = 0.1 ∘ ). Moreover, electric field-dependent fringe visibility is observed, which can be tuned by E 0 and θ. The potential barriers arising from a spatially modulated electric field are observed to cause significant distortions in the Talbot patterns when the modulation length ( <?CDATA λ′\lambda^{\prime}λ′?> λ ′ ) is equal to the de Broglie wavelength ( <?CDATA λdB\lambda_\mathrm{dB}λdB​?> λ d B ). Sidebands are observed in the Talbot pattern due to the efficient transfer of energy from the oscillating field to the wave packet when the frequency of oscillation (ω) is of the order of ω 0 ( <?CDATA $ = 2\pi/T_0$?> = 2 π / T 0 ), where T 0 is the interaction time. This study will be helpful in uniform electric field-controlled precision metrology, developing a highly sensitive electric field sensor based on Talbot interference, and precisely aligning the matter wave optical setup. Furthermore, the sidebands in the Talbot fringe can be used as a precise tool for momentum splitter in matter wave interferometry.
We examine how partial coherence and wavefront curvature of beams affect interference fringes behind diffraction gratings. We simulate (1) the Talbot effect, (2) far-field diffraction, (3) Mach-Zehnader interferometers, (4) Talbot-Lau interferometers, and (5) Lau interferometers using a numerically efficient expression. We show how interference fringes in each case depend on the beam's initial width, its coherence width (transverse coherence length), and its wavefront curvature in directions both parallel and perpendicular to the grating bars. The separation between gratings and the rotational alignment of the gratings about the optical axis are also considered. The formula used for our simulations is derived using the mutual intensity function of a Gaussian Schell-model beam.
We demonstrate a near-field Talbot-Lau interferometer for C70 fullerene molecules. Such interferometers are particularly suitable for larger masses. Using three free-standing gold gratings of 1 microm period and a transversally incoherent but velocity-selected molecular beam, we achieve an interference fringe visibility of 40% with high count rate. Both the high visibility and its velocity dependence are in good agreement with a quantum simulation that takes into account the van der Waals interaction of the molecules with the gratings and are in striking contrast to a classical moiré model.
We discuss modern developments in quantum optics with organic molecules, clusters and nanoparticles -- in particular recent realizations of near-field matter-wave interferometry. A unified theoretical description in phase space allows us to describe quantum interferometry in position space and in the time domain on an equal footing. In order to establish matter-wave interferometers as a universal tool, which can accept and address a variety of nanoparticles, we elaborate on new quantum optical elements, such as diffraction gratings made of matter and light, as well as their absorptive and dispersive interaction with complex materials. We present Talbot-Lau interferometry (TLI), the Kapitza-Dirac-Talbot-Lau interferometer (KDTLI) and interferometry with pulsed optical gratings (OTIMA) as the most advanced devices to study the quantum wave nature of composite matter. These experiments define the current mass and complexity record in interferometric explorations of quantum macroscopicity and they open new avenues to quantum assisted metrology with applications in physical chemistry and biomolecular physics.