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Physics Letters A

Aharonov–Casher phase shift and the change in velocity of a moving magnet traversing an electric field

Norman Henry March

Published Oct 21, 2006• 2 citations
Publisher
DOI
10.1016/j.physleta.2006.10.036

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Motivated by the theoretical work of Boyer [J. Phys. A: Math. Gen. 39 (2006) 3455] plus the quite recent interferometric experiment of Shinohara, Aoki and Morinaga [Phys. Rev. A66 (2002) 042106] in which the scalar Aharonov-Bohm effect was studied, we re-open the extension to neutral particles carrying a magnetic moment and passing through a region of intense electric field, treated theoretically by Aharonov and Casher (AC) and independently by Anandan. An alternative interpretation of results on (a) neutrons and (b) TlF molecules to that afforded by AC is shown to involve only (i) the de Broglie wavelength of matter waves and (ii) the prediction from Maxwell’s equations for the change in velocity of a neutral moving magnet as it enters or leaves an electric field. The exquisite sensitivity of experiment (b) allows a fractional change in velocity of order 10 15 to be quantitatively determined.

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In this paper we give a covariant expression for Aharonov–Casher phase. This expression is a combination of the canonical electric field, Aharonov–Casher phase plus a magnetic field phase shift. We use this covariant expression for the Aharonov–Casher phase to investigate the case of a neutral particle with a non-zero magnetic moment moving in the time dependent electric and magnetic fields of a plane electromagnetic wave background. We focus on the case where the magnetic moment of the particle is oriented so that both the electric and magnetic fields lead to non-zero phases, and we look at the interplay between these electric and magnetic phases.

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When a moving magnetic dipole enters a strong electric field the velocity of the magnet changes by a tiny amount. When a polarized, coherent beam of magnetic particles is split, the two parts passed through strong electric fields of opposite sign, then rejoined, interference patterns are observed due to the phase shift between the de Broglie waves of the two branches. Two recent, extremely delicate experiments, one using neutron interferometry and the second using F nuclei in TlF molecules, are reviewed and interpreted in this way. The fractional velocity change was 1 part in for the neutrons and 1 in for the TlF molecules. This explains the phase shift discussed by Aharonov and Casher and, contrary to their statement, is not equivalent to an Aharonov - Bohm effect. The latter requires that a de Broglie wave phase shift be produced by a vector potential in the absence of a field.
Motivated by the theoretical work of Boyer [J. Phys. A: Math. Gen. 39 (2006) 3455] plus the quite recent interferometric experiment of Shinohara, Aoki and Morinaga [Phys. Rev. A66 (2002) 042106] in which the scalar Aharonov-Bohm effect was studied, we re-open the extension to neutral particles carrying a magnetic moment and passing through a region of intense electric field, treated theoretically by Aharonov and Casher (AC) and independently by Anandan. An alternative interpretation of results on (a) neutrons and (b) TlF molecules to that afforded by AC is shown to involve only (i) the de Broglie wavelength of matter waves and (ii) the prediction from Maxwell’s equations for the change in velocity of a neutral moving magnet as it enters or leaves an electric field. The exquisite sensitivity of experiment (b) allows a fractional change in velocity of order 10 15 to be quantitatively determined.
In this paper we give a covariant expression for Aharonov–Casher phase. This expression is a combination of the canonical electric field, Aharonov–Casher phase plus a magnetic field phase shift. We use this covariant expression for the Aharonov–Casher phase to investigate the case of a neutral particle with a non-zero magnetic moment moving in the time dependent electric and magnetic fields of a plane electromagnetic wave background. We focus on the case where the magnetic moment of the particle is oriented so that both the electric and magnetic fields lead to non-zero phases, and we look at the interplay between these electric and magnetic phases.