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Physical Review A

Experimental confirmation of Aharonov-Bohm effect using a toroidal magnetic field confined by a superconductor

Nobuyuki Osakabe, Tsuyoshi Matsuda, Takeshi Kawasaki, Junji Endo, Akira Tonomura, S. Yano, Hiroji Yamada

Published Aug 1, 1986• 205 citations
Publisher

Abstract

The electron holography technique was employed to make a crucial test of the existence of the Aharonov-Bohm (AB) effect. The relative phase shift was measured between two electron waves passing through spaces inside and outside a tiny toroidal ferromagnet, covered completely with a superconductor layer and a Cu layer. Below the transition temperature the relative phase shift was measured to be 0 or \ensuremath{\pi} due to the magnetic-flux quantization in units of h/2e. The results directly demonstrated the existence of the AB effect even when the magnetic field was confined by the surrounding superconductor due to the Meissner effect and an electron beam was prevented from penetrating the magnet.

DOI
10.1103/physreva.34.815

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In the Aharonov–Bohm (AB) effect, electrons form an interference pattern whose bright and dark fringes shift position when the magnetic flux confined within a nearby solenoid is changed, even though the electrons travel only through regions where the magnetic field is zero. Operationally, the experiment compares electron interference patterns obtained under different solenoid current (or enclosed flux) conditions, revealing a measurable phase difference—observed as fringe displacement—between the two electron paths despite the absence of any force acting on the electrons along those paths. Each electron arrives as a dot, but many dots build up the interference pattern. The effect tracks the enclosed flux (current level), with on/off as an illustrative extreme. What is measured is phase difference / fringe displacement, i.e., a relative effect between the two paths. This Aharonov-Bohm effect is famous in modern physics and widely regarded as proof that electromagnetic potentials possess physical reality even in regions where fields vanish. This paper reinterprets the AB effect by reframing it using the SP3 (space-phase) theory.

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The electron holography technique was employed to make a crucial test of the existence of the Aharonov-Bohm (AB) effect. The relative phase shift was measured between two electron waves passing through spaces inside and outside a tiny toroidal ferromagnet, covered completely with a superconductor layer and a Cu layer. Below the transition temperature the relative phase shift was measured to be 0 or \ensuremath{\pi} due to the magnetic-flux quantization in units of h/2e. The results directly demonstrated the existence of the AB effect even when the magnetic field was confined by the surrounding superconductor due to the Meissner effect and an electron beam was prevented from penetrating the magnet.
The Aharonov-Bohm (AB) effect was tested under conditions where an electron wave and a magnetic field did not overlap: the Meissner effect of the superconductor shielding a toroidal ferromagnet eliminated the leakage field. Using the newly-developed technique of electron holography, conclusive evidence for the AB effect was obtained by detecting a relative phase shift of π between the two electron waves passing through the hole and outside the toroid. The detected phase shift value of exactly π comes from the quantization of the magnetic flux within the superconductor. This quantization assures the complete shielding of the magnetic field.
Evidence for the Aharonov-Bohm effect was obtained with magnetic fields shielded from the electron wave. A toroidal ferromagnet was covered with a superconductor layer to confine the field, and further with a copper layer for complete shielding from the electron wave. The expected relative phase shift was detected with electron holography between two electron beams, one passing through the hole of the toroid, and the other passing outside. The experiment gave direct evidence for flux quantization also.
Predictions made by Aharonov and Bohm concerning the effects of electromagnetic potentials on electrons in field-free regions of space, have been demonstrated in superconductors with the use of the flux produced by a very fine toroidal solenoid. The use of a toroidal geometry sidesteps the objections raised by Roy concerning the use of sources of flux with linear geometries. The use of superconductors excludes the possibility that stray electrons can pass through the flux-filled region of space to produce the observed phenomena.
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.
In the Aharonov–Bohm (AB) effect, electrons form an interference pattern whose bright and dark fringes shift position when the magnetic flux confined within a nearby solenoid is changed, even though the electrons travel only through regions where the magnetic field is zero. Operationally, the experiment compares electron interference patterns obtained under different solenoid current (or enclosed flux) conditions, revealing a measurable phase difference—observed as fringe displacement—between the two electron paths despite the absence of any force acting on the electrons along those paths. Each electron arrives as a dot, but many dots build up the interference pattern. The effect tracks the enclosed flux (current level), with on/off as an illustrative extreme. What is measured is phase difference / fringe displacement, i.e., a relative effect between the two paths. This Aharonov-Bohm effect is famous in modern physics and widely regarded as proof that electromagnetic potentials possess physical reality even in regions where fields vanish. This paper reinterprets the AB effect by reframing it using the SP3 (space-phase) theory.