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IEEE Transactions on Instrumentation and Measurement

Measurement of Berry's Phase for Partial Cycles Using a Time-Domain Atomic Interferometer

Makoto Yasuhara, T. Aoki, Hirotaka Narui, Atsuo Morinaga

Published Mar 21, 2005• 3 citations
Publisher

Abstract

The Berry phase of atom for partial cycles of rotating magnetic field in parameter space was successfully measured free from the dynamical phase shift by using a time-domain sodium atom interferometer. The obtained phase shift was in an agreement with the prediction of Berry's phase for partial cycles.
DOI
10.1109/tim.2005.843564

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Journal of the Physical Society of Japan•Oct 25, 2013•3 citations
Berry's phase of the atom in the state with a positive or negative ggg factor for partial cycles of a rotating magnetic field was determined free from the dynamical phase shift using a time-domain atom interferometer. The experimental phase shift is in good agreement with the prediction of Berry's phase for partial cycles. It was found that the sense of Berry's phase depends on the sign of the magnetic quantum number, the sense of the rotating magnetic field, and the sign of the ggg factor of the state.
We present a concept for measuring a Berry phase using an atom interferometer in an optical Ramsey arrangement. The adiabatic cyclic process needed for the appearance of a Berry phase consists of the adiabatic change of population in one of the interferometer arms. A closed circuit in parameter space is realized by the time-dependent Doppler detuning of two additional strongly focused Gaussian beams, which couple selectively to one of the interferometer arms. It is shown that the resulting additional atomic phase consists of a Berry phase corresponding to the phase difference of the two Gaussian beams and a dynamical phase caused by the dynamical Stark effect. By recombining the two interferometer arms this total phase gives rise to a shift of the interference pattern. In case of a Ramsey arrangement with magnesium atoms the parameters of an experimental realization have been calculated. Further improvements using laser-cooled and trapped atoms are discussed.
Using a magnetic-field-insensitive two-photon transition, the phase shift of atomic interference fringes and the frequency shift of the resonance spectrum were examined for a noncyclic rotation of a magnetic field during the interrogation time of an atom interferometer. We observed a phase shift proportional to the rotation angle of the magnetic field when the initial state and the final state were subjected to interference. We confirmed that the phase shift is equivalent to the scalar Aharonov-Bohm phase due to the geometrical potential. On the other hand, we demonstrated that the noncyclic Berry phase defined by the geodesic gauge is measurable using a strategy that the magnetic field rapidly returns to the initial direction during the interrogation time of the atom interferometer.
We demonstrated the noncyclic Berry phase based on the geodesic rule proposed by Samuel and Bhandari using two dynamical phase-free systems in a spin-redirection evolution. In the atom interferometer with a noncyclic rotating magnetic field, the quasi-geodesic arc was realized by a straight line connecting the initial and the final points. The phase shifts were measured for noncyclic evolutions and cyclic evolutions connected by several quasi-geodesic arcs. The other system to observe the noncyclic Berry phase for change in the propagation direction of light was a single mode fiber wounded on an auxiliary cylinder to realize strictly back along the real geodesic arc joining the final to the initial point. Theses observed phase shifts were in good agreement with the theoretical values of the noncyclic Berry phase based on the geodesic rule.