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Physical Review Letters

Measurement of the He-McKellar-Wilkens Topological Phase by Atom Interferometry and Test of Its Independence with Atom Velocity

Jonathan Gillot, S. Lepoutre, A. Gauguet, M Büchner, J. Vigué

Published Jul 15, 2013• 38 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.111.030401

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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.
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.
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.
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 measured the tune-out wavelength of lithium isotope 7Li^{7}\mathrm{Li}7Li at 671 nm. We have used our atom interferometer to measure the phase shift due to the dynamical Stark effect as a function of the laser frequency when a laser beam was focused on a single interferometer arm. The tune-out wavelength is a function of the hyperfine F,mFF,{m}_{F}F,mF​ sublevel, and we have prepared the atoms in the sublevel F=2,mF=+2F=2,{m}_{F}=+2F=2,mF​=+2 or $\ensuremath{-}2$. We find that the tune-out frequency of the F=2,mF=+2F=2,{m}_{F}=+2F=2,mF​=+2 sublevel is at 3388(8)MHz3388(8)\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}3388(8)MHz to the blue of the $^{2}S_{1/2},F=1\ensuremath{\rightarrow}^{2}P_{1/2},{F}^{\ensuremath{'}}=2$ transition, the accuracy of this measurement being limited by imperfect optical pumping. This measurement is in excellent agreement with its theoretical value, and, once corrected for different tensorial contributions, our measurement agrees with the more precise measurement of Copenhaver et al. [Phys. Rev. A 100, 063603 (2019)], who also used atom interferometry but different experimental conditions.