Direct measurement of the Aharonov-Casher phase and tensor Stark polarizability using a calcium atomic polarization interferometer

An atomic polarizing white-color interferometer composed of the wave packets in the $m=+1\mathrm{}$ and $m=-1$ states of the excited ${}^3{P}_1$ 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 ${}^3{P}_1$ state was determined to be ${\alpha }_2=2.623\mathrm{}\pm 0.015\hspace{0.5em}\mathrm{k}\mathrm{H}\mathrm{z}/(\mathrm{k}\mathrm{V}/\mathrm{c}\mathrm{m}{)}^2$ from the frequency shift between the $m=+1\mathrm{}$ and $m=-1$ states.