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Conference on Precision Electromagnetic Measurements

Measurement of Berry's Phase using a Time-Domain Atom Interferometer

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

Published Jun 1, 2004• 0 citations
Publisher

Abstract

We propose a novel method of the measurement of Berry's phase free from the dynamical phase shift for partial cycles of rotating magnetic field in parameter space by using a time-domain atom interferometer. The experimental results are presented and discussed
DOI
10.1109/cpem.2004.305320

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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.
We report on the demonstration of Berry's phase in an atomic state interacting with a laser field. We draw an analogy between this system and that of a spin interacting with a directionally varying magnetic field. This allows us to identify an effective magnetic quantum number for the atom-light system that governs the maximum Berry phase the atomic state can acquire. We realize two systems that have different effective magnetic quantum numbers, and use a recently developed atom interferometer to make measurements of Berry's phase.
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.