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International Journal of Modern Physics B

QUANTUM PHENOMENA VISUALIZED BY ELECTRON WAVES

Akira Tonomura

Published Dec 30, 2007• 1 citation
Publisher

Abstract

Quantum phenomena have become directly observable with the development of advanced techniques such as coherent field-emission electron beams, sensitive detectors, and microlithography. Examples are the single-electron build-up of an interference pattern, which contains, as R. Feynman describes in his textbook, the heart of quantum mechanics, and the Aharonov–Bohm (AB) effect, which indicates the physical significance of gauge fields. Using the AB effect, i.e., the fundamental principle behind the interaction of an electron wave with electromagnetic fields, new ways to directly observe previously unobservable microscopic quantum objects and phenomena were developed by detecting the phase of electrons.

DOI
10.1142/s021797920703837x

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Quantum phenomena have become directly observable with the development of advanced techniques such as coherent field-emission electron beams, sensitive detectors, and microlithography. Examples are the single-electron build-up of an interference pattern, which contains, as R. Feynman describes in his textbook, the heart of quantum mechanics, and the Aharonov–Bohm (AB) effect, which indicates the physical significance of gauge fields. Using the AB effect, i.e., the fundamental principle behind the interaction of an electron wave with electromagnetic fields, new ways to directly observe previously unobservable microscopic quantum objects and phenomena were developed by detecting the phase of electrons.
Electron interference phenomena are now easily observable with the advent of bright and yet coherent field-emission electron beams. The interaction of electron waves with electromagnetic fields is essentially described by the Aharonov–Bohm (AB) effect. However, the AB effect has long been disputed due to a feature that cannot be understood in terms of classical electrodynamics. This paper describes the experiments that confirmed its existence and discusses its expanding applications to the observation of electromagnetic fields in the microscopic region.
This article describes the Aharonov-Bohm (AB) effect of electron waves travelling in free space and its application to the observation of gauge fields (vector potentials). The AB effect is inconceivable in classical physics since an observable effect is produced on electrons passing through field-free spaces. Electrons can be affected only by Lorentz forces due to electromagnetic fields. The situation is different in quantum mechanics, where electrons show wave properties: the concept of force is no longer relevant, so electric field E and magnetic field B, defined as forces acting on a unit charge, take on secondary meanings. “Phase shifts” come into play, and the primary physical entities become neither E nor B but electrostatic potential V and vector potential A. These potentials interact with electron waves and shift their phases.
Fundamental aspects of quantum mechanics, which were discussed only theoretically as "thought experiments" in the 1920s and 1930s, have begun to frequently show up in nanoscopic regions owing to recent rapid progress in advanced technologies. Quantum phenomena were once regarded as the ultimate factors limiting further miniaturization trends of microstructured electronic devices, but now they have begun to be actively used as the principles for new devices such as quantum computers. To directly observe what had been unobservable quantum phenomena, we have tried to develop bright and monochromatic electron beams for the last 35 years. Every time the brightness of an electron beam improved, fundamental experiments in quantum mechanics became possible, and quantum phenomena became observable by using the wave nature of electrons.
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
The nature of the problem The quantum world is inexplicable in classical terms. The predictions pertaining to the interaction of matter and light embodied in Newton's laws for the motion of particles and Maxwell's equations governing the propagation of electromagnetic fields are in flat contradiction with the experimental facts at the microscopic scale. A key feature of quantum effects is their apparent indeterminism, that individual atomic events are unpredictable, uncontrollable and literally seem to have no cause. Regularities emerge only when one considers a large ensemble of such events. This indeed is generally considered to constitute the heart of the conceptual problem posed by quantum phenomena, necessitating a fundamental revision of the deterministic classical world view. Some of the principal phenomena, among those discussed in this book, are as follows: ( a ) Self-interference: a beam of electrons sent one at a time through a barrier containing two apertures builds up through a series of localized detection events on a screen an interference pattern characteristic of waves (cf. the frontispiece and §5.1). ( b ) Tunnelling: an α-particle trapped in a nucleus can pass through a potential barrier in a manner forbidden to a classical particle (§5.3). ( c ) The stability of matter: atoms and molecules are found to exist only in certain discrete, or ‘stationary’, energy states. For this reason they do not ‘collapse’, the result predicted by classical electrodynamics. During transitions between stationary states (quantum jumps) an atom exchanges a discrete quantity of energy with the electromagnetic field (§§4.5, 7.6). […]