Comment on Experiments Related to the Aharonov–Bohm Phase Shift

Michel Bawin, André Burnel

Kicheon Kang

We investigate the role of Faraday's law of induction manifested in the quantum state of Aharonov-Bohm (AB) loops. In particular, a flux-switching experiment is proposed for a double-dot AB loop to verify the phase shift induced by Faraday's law. The induced Faraday phase is shown to be geometric and nontopological. This study demonstrates that the relation between the local phases of a ring at different fluxes is not arbitrary but is instead determined by Faraday's inductive law, which is in contrast to the arbitrary local phase of an AB loop for a given flux.

Timothy H. Boyer

In 1984 Aharonov and Casher proposed that a beam of neutral particles with magnetic dipole moments passing around opposite sides of a line charge will undergo a relative quantum phase shift. This is currently under experimental investigation. Aharonov and Casher claimed that the magnetic dipole particles should undergo the phase shift despite experiencing no classical force. They suggested that this new effect has a ``duality'' with the solenoid Aharonov-Bohm effect where charged particles passing around a magnetic solenoid experience a phase shift despite, it is claimed, experiencing no classical force. Here it is pointed out that a magnetic dipole particle passing a line charge does indeed experience a classical electromagnetic force in the usual electric-current model for a magnetic dipole. This force will produce a relative lag between dipoles passing on opposite sides of the line charge, and the classical lag then leads to a quantum phase shift in exact agreement with that calculated by Aharonov and Casher. Thus actually the proposed Aharonov-Casher effect has a transparent explanation as a classical lag effect. It is emphasized that the solenoid Aharonov-Bohm effect is currently the only phase-shift effect which cannot be explained in an obvious fashion as arising from a classical lag and it is again proposed that also this shift may actually involve a classical electromagnetic lag effect. A natural experimental consequence suggested by the lag point of view is the breakdown of the interference pattern when the lag becomes comparable to the wave-packet coherence length.

Vladimir A. Namiot

Heinz J. Rothe

William Moreau, Dennis K. Ross

A complementary electric Aharonov-Bohm (AB) effect is proposed and investigated where one branch of a chopped and split electron beam traverses a region with an electric field and upon interference with the other branch no phase shift would be observed. The analysis of the proposed experiment is carried out (1) in a semiclassical (SC) eikonal approximation and (2) in a complete quantum-mechanical (QM) calculation with a plane-wave approximation similar to AB's original paper. The QM phase shift is the sum of the SC phase shift plus an AB-like phase shift for a constant potential. While the SC analysis predicts that there must be a phase shift, the full QM indicates that a null phase shift is possible.