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Electron matter optics and an electron Mach -Zehnder interferometer

Glen Gronniger

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

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.

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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.
Since the advent of quantum mechanics and the idea that massive particles exhibit wave properties, physicists have made efforts to make use of the short deBroglie wave length of matter waves for fundamental as well as practical studies. Among these are the precise measurements allowed by interference, diffraction, and microscopy as well as the study of more fundamental aspects of quantum theory such as the Aharonov-Bohm effects or the Stern-Gerlach effect, which are described below. However, in order to use matter waves to observe any of these effects it is necessary to produce and maintain coherence in the waves which are used for measurement. With a grasp of what coherence is and how it may be achieved and maintained one can move forward to study the interesting phenomena associated with coherent matter waves. More specifically in this work the interference and diffraction of electron matter waves are considered. The phenomena under consideration are those associated with the interaction of the electric charge and magnetic dipole moment of the electron with external fields and potentials while in the process of interfering or diffracting. Namely the focus of this dissertation is the Aharonov-Bohm effect, the Aharonov-Casher effect, and the Stern-Gerlach effect. Additionally, a wide-angle electron beam-splitter capable of producing two centimeter beam separation at the detection plane is discussed. The beam-splitter utilizes a nanofabricated periodic grating in combination with a bi-prism element. Contrary to devices utilizing only bi-prism elements, the use of the periodic grating causes amplitude, and not wave front, splitting. Even at maximum separation, beam profiles remain undistorted, providing evidence that coherence is intact. This is a step towards the realization of a large area electron interferometer using such a grating bi-prism combination. Such an interferometer could, in principle, be used to test the dispersionless nature of the Aharonov-Bohm effect. Work towards such an interferometer and possible future work are also discussed. Advisor: Herman Batelaan
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
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.
In 1924 Louis de Broglie introduced the concept of wave-particle duality: the Planck constant hhh relates the momentum ppp of a massive particle to its de Broglie wavelength λ=h/pλ=h/pλ=h/p. The superposition principle is one of the main postulates of quantum mechanics; diffraction and interference phenomena are therefore predicted and have been observed on objects of increasing complexity, from electrons to neutrons and molecules. Beyond the early electron diffraction experiments, the demonstration of single-electron double-slit-like interference was a highly sought-after result. Initially proposed by Richard Feynman as a thought experiment it was finally carried out in 1976. A few years later, positron diffraction was first observed. However, an analog of the double-slit experiment has not been performed to date on any system containing antimatter. Here we present the first observation of matter wave interference of single positrons, by using a period-magnifying Talbot-Lau interferometer based on material diffraction gratings. Individual positrons in the 8-14 keV energy range from a monochromatic beam were detected by high-resolution nuclear emulsions. The observed energy dependence of fringe contrast proves the quantum-mechanical origin of the detected periodic pattern and excludes classical projective effects. Talbot-Lau interferometers are well-suited to the experimental challenges posed by low intensity antimatter beams and represent a promising option for measuring the gravitational acceleration of neutral antimatter.
Although interferometry's earliest and most familiar use is with photons, the discovery of matter-wave (deBroglie-wave) interference for electrons demanded the development of quantum mechanics. Since then, matter-wave interferometry has been performed with neutrons, Cooper electron-pairs, and most recently, with whole atoms and diatomic molecules. This talk describes our recent high-flux atom interferometry experiments using the generalized Talbot-vonLau effect. Our interferometer consists of a sequence of three planar vacuum-slit diffraction gratings, microfabricated from silicon nitride membranes. DeBroglie-wave interference fringes are sensed by measuring the transmission of potassium atoms on a hot- wire as a function of grating relative position. Different spatial Fourier components (up to sixth) in the diffraction pattern are resonant in the interferometer at different atomic velocities (i.e., at different wavelengths). When a laser cooled slow atomic beam is incident, various different diffraction patterns are observed as a function of atomic velocity. In an alternative `Heisenberg Microscope' configuration an incident thermal beam produces a velocity average over different fringe Fourier components. AC modulated weak laser light passing through the interferometer interacts selectively with atoms at a specific velocity. The associated fringe pattern is then ac modulated and revealed by its selective destruction.
Here, we experimentally demonstrate interaction-free measurements with electrons using a novel electron Mach-Zehnder interferometer. The flexible two-grating electron interferometer is constructed in a conventional transmission electron microscope and achieves high contrast in discrete output detectors, tunable alignment with independently movable beam splitters, and scanning capabilities for imaging. With this path-separated electron interferometer, which closely matches theoretical expectations, we demonstrate electron interaction-free measurements with an efficiency of 14±1%. Implementing this quantum protocol in electron imaging opens a path toward interaction-free electron microscopy.