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Physical Review Letters

Measurement of the Aharonov-Casher phase in an atomic system

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

Published Nov 29, 1993• 129 citations
Publisher

Abstract

We describe a new experimental configuration suitable for observing the topological 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 electric field and we have verified the predicted size of the effect with an accuracy of 4%.

DOI
10.1103/physrevlett.71.3641

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We describe a new experimental configuration suitable for observing the topological 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 electric field and we have verified the predicted size of the effect with an accuracy of 4%.
We report an experimental test of the topological phase predicted by He and McKellar in 1993 and by Wilkens in 1994: this phase, which appears when an electric dipole propagates in a magnetic field, is connected to the Aharonov-Casher effect by electric-magnetic duality. The He-McKellar-Wilkens phase is quite small, at most 27 mrad in our experiment, and this experiment requires the high phase sensitivity of our atom interferometer with spatially separated arms as well as symmetry reversals such as the direction of the electric and magnetic fields. The measured value of the He-McKellar-Wilkens phase differs by 31% from its theoretical value, a difference possibly due to some as yet uncontrolled systematic errors.
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).
We have recently tested the topological phase predicted by He and McKellar and by Wilkens: this phase appears when an electric dipole propagates in a transverse magnetic field. In the present paper, we first recall the physical origin of this phase and its relations to the Aharonov-Bohm and Aharonov-Casher phases. We then explain possible detection schemes and we briefly describe the lithium atom interferometer we have used for this purpose. Finally, we analyze in great detail the phase shifts induced by electric and magnetic fields acting on such an interferometer, taking into account experimental defects. The experiment and its results are described in the following paper.