We present an atomic multiwave interferometer with magnetic sublevels to precisely determine the Aharonov-Casher (AC) geometric phase. Simulations show that this interferometer has sharper fringes than a normal two-wave interferometer, which means a higher phase resolution can be achieved. Moreover, atoms evolving in a single hyperfine structure state make the interferometer insensitive to the dc Stark phase shift. This dc Stark shift is one of the main noise sources in AC phase measurements. The constraint of the photon rest mass is also discussed when using this atomic interferometer to measure the Aharonov-Casher phase.
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.
An atomic polarizing white-color interferometer composed of the wave packets in the
m=+1 and $m=\ensuremath{-}1$ states of the excited
3P1 state of Ca, has been developed using a thermal atomic beam excited by a pair of two resonant lights at two separate zones under a homogeneous magnetic field. The interferometer generated the Ramsey fringes as a detuning of the rf frequency between two resonant lights from the Zeeman-frequency shift, while it generates white-color interference fringes as a detuning of laser frequency. The interferometer was used for the direct and short-time measurement of the Aharonov-Casher phase by removing the main part of dc Stark phase shift and without the influence of the frequency fluctuation of a laser. The measured dependence of the Aharonov-Casher phase on the electric field agreed with the predicted one within a relative uncertainty of 2.9%. The tensor polarizability in the
3P1 state was determined to be ${\ensuremath{\alpha}}_{2}=2.623\ifmmode\pm\else\textpm\fi{}0.015 \mathrm{k}\mathrm{H}\mathrm{z}/(\mathrm{k}\mathrm{V}/\mathrm{c}\mathrm{m}{)}^{2}$ from the frequency shift between the
m=+1 and $m=\ensuremath{-}1$ states.