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Physical Review A

Aharonov-Casher phase in an atomic system

Karin Sangster, Edward A. Hinds, Stephen Mark Barnett, Erling Riis, Alastair G. Sinclair

Published Mar 1, 1995• 59 citations
Publisher

Abstract

We describe an experimental configuration suitable for observing the geometric phase of Aharonov and Casher in atomic systems. Using this we have been able to show experimentally that the Aharonov-Casher phase is both independent of velocity and proportional to an electric field and we have verified the predicted size of the effect with an accuracy of 2%.

DOI
10.1103/physreva.51.1776

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We describe an experimental configuration suitable for observing the geometric phase of Aharonov and Casher in atomic systems. Using this we have been able to show experimentally that the Aharonov-Casher phase is both independent of velocity and proportional to an electric field and we have verified the predicted size of the effect with an accuracy of 2%.
It is demonstrated that the Aharonov-Casher (AC) phase is a geometric phase that, in general, depends on the details of the closed path taken by a particle with a magnetic moment that is subject to an electric field. Consequently, it is not a topological phase. The proof of this statement is obtained by developing a counterexample that elucidates the dependence of the AC phase on the details of the path. Furthermore, we demonstrate that, in the particular example considered here, paths having an Abelian AC phase factor, also have an AC phase that is path-independent, whereas paths having a non-Abelian AC phase factor may have an AC phase that is path-dependent (i.e., not topological).
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.