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Journal of Physics A Mathematical and General

Aharonov-Casher effect and geometrical phases

R Mignani

Published Apr 21, 1991• 25 citations
Publisher

Abstract

The phaseshift experienced by a neutral particle with a magnetic moment as it encircles an infinite line of charge (Aharonov-Casher effect) (1984) is derived as a special case of geometrical phases, i.e. the standard Berry phase and the gauge-invariant Yang phase.
DOI
10.1088/0305-4470/24/8/006

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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.
The usual vector Aharonov–Bohm effect involves the quantum interference of electrons encircling a solenoid due to the magnetic vector potential. The analogous Aharonov–Casher effect was predicted for the neutron, which carries a magnetic dipole moment, encircling a line of electric charge . It was first observed by neutron interferometry, as described in this chapter. An analogous effect using neutrons and a pulsed magnetic solenoid in one leg of the interferometer has also been observed. This experiment using both polarized and unpolarized neutrons is described in this chapter. It is the first observation of the scalar Aharonov-Bohm effect. The idea of geometric phases was later shown to be pervasive in physics. These ideas were brought to full fruition in a neutron interferometry experiment in the late 1990s. The connections of this experiment with the helical field experiment of Bitter and Dubbers and the absorption experiment of Hasegawa are also discussed. The confinement-induced phase when neutrons move between narrow plates is another example of a non-local interaction of neutrons.
The relation of the Aharonov-Casher (AC) effect and the force on a particle having a magnetic moment is explored. The general form of the AC Hamiltonian is derived using the Foldy-Wouthuysen transformation to the Dirac equation. Geometries in which an analytic expression for the phase can be obtained are examined, as well as the relation of the AC phase to the Berry phase. The AC phase is determined for an arbitrary homogeneous electric field; it is quadratic (linear) in the field strength for small (large) electric field strengths.
The relation of the Aharonov-Casher (AC) effect and the force on a particle having a magnetic moment is explored. The general form of the AC Hamiltonian is derived using the Foldy-Wouthuysen transformation to the Dirac equation. Geometries in which an analytic expression for the phase can be obtained are examined, as well as the relation of the AC phase to the Berry phase. The AC phase is determined for an arbitrary homogeneous electric field; it is quadratic (linear) in the field strength for small (large) electric field strengths.
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.