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arXiv:1305.7267

A charged particle Talbot-Lau interferometer and magnetic field sensing

Roger Bach, Glen Gronniger, Herman Batelaan

Published May 30, 2013• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1305.7267

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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.
We study in detail a peculiar configuration of the Talbot-Lau matter wave interferometer, characterized by unequal distances between the two diffraction gratings and the observation plane. We refer to this apparatus as the ``asymmetric Talbot-Lau setup.'' Particular attention is given to its capabilities as an inertial sensor for particle and atomic beams, also in comparison with the classical moir\'e deflectometer. The present paper is motivated by possible experimental applications in the context of antimatter wave interferometry, including the measurement of the gravitational acceleration of antimatter particles. Therefore we focus our analysis on the current state of the art. To support our findings, we have also performed numerical simulations of realistic particle beams with varying speed distributions.
Quantum mechanics has fundamentally changed the way scientists think about the world. Quantum mechanical theory has found it's way into our everyday lives through advances in technology. In this dissertation a fundamental quantum mechanical demonstration and the technological development of a new quantum mechanical device are presented. Double-slit diffraction is a corner stone of quantum mechanics. It illustrates key features of quantum mechanics: interference and the particle-wave duality of matter. Here we demonstrate the full realization of Richard Feynman's famous thought experiment. By placing a movable mask in front of a double-slit to control the transmission through the individuals slits. Probability distributions for single- and double-slit arrangements were observed. Additionally, by recording single electron detection events diffracting through a double-slit,a diffraction pattern was built up from individual events. Additionally, a demonstration of a three grating Talbot-Lau interferometer for electrons is presented. As a proof of principle the interferometer is used to measure magnetic fields. The possibility to extend this work to build a scaled-up electron interferometer for sensitive magnetic field sensing is discussed. A theoretical model is presented to simulate the two experiments. This model is developed from Richard Feynman's path integral formalism, where a wave function is propagated through the elements of the system. The theoretical simulations reproduce the experimental data well, except for a large discrepancy of a factor of 5.5 between the experimental and theoretical sensitivity of the Talbot-Lau interferometer. The origin of the discrepancy is currently unknown. These experiments were built off of previous work done here at the University of Nebraska-Lincoln, and improvements to the preexisting system are discussed. While these experiments likely did not demonstrate anything contrary to conventional quantum mechanics, it is important to continually probe these types of experiments to test the fundamental principles of quantum mechanics and explore it's technical applications. Advisor: Herman Batelaan
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.
The Talbot-Lau interferometer is a proven tool to perform measurements in the near-field regime. It has been extensively used for investigating the wave nature of electrons, atoms, and complex organic molecules. However, when designing devices with high geometrical acceptances, which would be desirable when dealing with low-intensity sources of particles, the alignment requirements become much more stringent. Furthermore, if the particles are charged, the influence of external fields becomes quickly non-negligible when increasing the length of the device. This paper focuses on both the geometric and physical constraints of an ion Talbot-Lau interferometer, with emphasis on the scaling of such constraints with the size of the device. Mathematical formulas which set limits on the critical parameters are derived and applied to a test setup for protons.
Abstract A setup with three equally spaced transmission gratings can be described as a moiré deflectometer in the classical regime and as a Talbot–Lau interferometer in the quantum regime. We successfully operate such a three-grating device with a de Broglie wavelength span of more than two orders of magnitude (20 fm to 2.2 pm), employing different particles such as xenon, krypton, argon, helium, and hydrogen. With that we directly observe the transition from the classical description with fast xenon atoms, to the characteristic quantum behaviour of the Talbot–Lau interferometer using hydrogen atoms with correspondingly long de Broglie wavelength. The systematic study of the interference pattern gives important insights in the feasibility of a proton or antiproton interferometer with this setup.
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.