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Proceedings of the Japan Academy Series B

The Aharonov-Bohm effect and its applications to electron phase microscopy

Akira Tonomura

Published Jan 1, 2006• 18 citations
Publisher

Abstract

The Aharonov-Bohm effect was conclusively established by a series of our electron interference experiments, with the help of some advanced techniques, such as coherent field-emission electron beams and microlithography. Using this fundamental principle behind the interaction of an electron wave with electromagnetic fields, new observation techniques were developed to directly observe microscopic objects and quantum phenomena previously unobservable.

DOI
10.2183/pjab.82.45

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The Aharonov-Bohm effect was conclusively established by a series of our electron interference experiments, with the help of some advanced techniques, such as coherent field-emission electron beams and microlithography. Using this fundamental principle behind the interaction of an electron wave with electromagnetic fields, new observation techniques were developed to directly observe microscopic objects and quantum phenomena previously unobservable.
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.
The AB (Aharonov-Bohm) effect is a pivotal quantum mechanical phenomenon that illustrates the fundamental role of the electromagnetic vector potential A in determining the phase of a charged particle's wave function, even in regions where the magnetic field B is zero.This effect demonstrates that quantum particles are influenced not only by the fields directly present but also by the potentials associated with those fields.In the AB effect, an electron beam is split into two paths, with one path encircling a solenoid and the other bypassing it.Despite the absence of a magnetic field in the regions traversed by the beams, the vector potential A associated with the magnetic flux  through the solenoid induces a phase shift in the electron's wave function.This phase shift, quantified by qc     , manifests as a change in the interference pattern observed in the detection screen.The phenomenon underscores the principle of gauge invariance in QED (quantum electrodynamics), where physical observables remain invariant under local gauge transformations of the vector and scalar potentials.This reinforces the notion that the vector potential A has a profound impact on quantum systems, beyond its classical role.This article outlines the AB effect, including its theoretical framework, experimental observations, and implications.The focus on the role of the vector potential in quantum mechanics provides a comprehensive understanding of this important phenomenon.
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.