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arXiv:1210.5697 · Physical Review Letters

He-McKellar-Wilkens Topological Phase in Atom Interferometry

S. Lepoutre, A. Gauguet, G. Trénec, M Büchner, J. Vigué

Published Sep 20, 2012• 65 citations
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Abstract

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.

DOI
10.1103/physrevlett.109.120404

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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.
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.
In this paper, we describe an experimental test of the He-McKellar-Wilkens (HMW) topological phase with our lithium atom interferometer. The expected value of the HMW phase shift in our experiment is small and its measurement was difficult because of stray phase shifts due to small experimental defects. We start by describing our setup and we characterize the effects of the electric and magnetic fields needed to observe the HMW effect. Then we develop a model of our interferometer signals including all the defects we have identified. After various tests of this model, we use it to suppress the majority of the stray phase shifts. We thus obtain a series of measurements of the HMW phase: the results are 31% larger than expected and this discrepancy is probably due to some limitations of our model.
In this Letter, we report a measurement of the He-McKellar-Wilkens (HMW) topological phase by atom interferometry. The experiment is done with our lithium atom interferometer, and in order to suppress the stray effects present in our first experiment, we use optical pumping of the (7)Li atoms in their F=2, m(F)=+2 (or -2) ground state sublevel. In these conditions, the measured phase shift is the sum of the HMW phase and of the Aharonov-Casher phase, which are separated due to their different m(F) dependence. The HMW phase has been measured for different lithium beam velocities and the results are in very good agreement with a phase independent of the atom velocity, as expected for a topological phase.
There are three topological phases related to electromagnetic interactions in quantum mechanics: 1. The Aharonov Bohm phase acquired when a charged particle encircles a magnetic field but travels through a field free region. 2. The Aharonov Casher phase acquired when a magnetic dipole encircles electric charges but travels through a charge free region. 3. The He McKellar Wilkens phase acquired when an electric dipole encircles magnetic charges but travels through a charge free region. We review the conditions under which these phases are indeed topological and their experimental realisation. Because the He McKellar Wilkens phase has been recently observed we pay particular attention to how the basic concept of "an electric dipole encircles magnetic charges" was realised experimentally, and discuss possible future experimental realisations.
We predict a quantum phase shift of a moving electric dipole in the presence of an external magnetic field at a distance. On the basis of the Lorentz-covariant field interaction approach, we show that a phase shift appears in the internal dipole state under the condition that the dipole is moving in the field-free region, which is distinct from the topological He-McKellar-Wilkens phase generated by a direct overlap of the dipole and the field. We discuss the experimental feasibility of detecting this phase with atomic interferometry and argue that detection of this phase will resolve the question of the locality in quantum electromagnetic interaction.