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Physical Review A

Noncyclic Berry phase and scalar Aharonov-Bohm phase for the spin-redirection evolution in an atom interferometer

Atsuo Morinaga, Kota Nanri

Published Aug 6, 2012• 7 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.86.022105

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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.
In a Ramsey atom interferometer excited by two electromagnetic fields, if atoms are under a time-varying scalar potential during the interrogation time, the phase of the Ramsey fringes shifts owing to the scalar Aharonov–Bohm effect. The phase shift was precisely examined using a Ramsey atom interferometer with a two-photon Raman transition under the second-order Zeeman potential, and a formula for the phase shift was derived. Using the derived formula, the frequency shift due to the scalar Aharonov–Bohm effect in the frequency standards utilizing the Ramsey atom interferometer was discussed.
The scalar Aharonov-Bohm effect with a time-dependent magnetic field was investigated for ultracold sodium atoms using the time-domain atom interferometer. The 38 interference fringes with almost the same amplitude verified the nondispersivity of this effect. The measured phase shift as a function of the strength of the applied magnetic field agreed with the predicted one within an accuracy of 3%. With a weak magnetic field orthogonal to the quantization axis, the phase shift was in proportion to the variation of the strength of the resultant magnetic field.
The $\ensuremath{\pi}$-phase shift between ∣F=1,mF=0⟩|F=1,{m}_{F}=0⟩∣F=1,mF​=0⟩ and ∣F=2,mF=0⟩|F=2,{m}_{F}=0⟩∣F=2,mF​=0⟩ states for an adiabatic rotation of a magnetic field observed in Ramsey atom interferometry arises from the negative sign of the transition amplitude between the ∣1,0⟩|1,0⟩∣1,0⟩ and ∣2,0⟩|2,0⟩∣2,0⟩ states when the wave functions are rotated to the opposite direction. Using a two-photon Raman atom interferometer with a cold ensemble of sodium atoms, the phase shift for a half-rotation of the magnetic field was confirmed to be $\ensuremath{\pi}\text{ }\text{rad}$ with an uncertainty of 4%, and the phase shift for a noncyclic adiabatic rotation of the magnetic field was investigated.
The phase shift and visibility of fringes in the Ramsey atom interferometer composed of the ∣F=1|F=1∣F=1,${m}_{F}=0\ensuremath{\rangle}$ and ∣F=2|F=2∣F=2,${m}_{F}=0\ensuremath{\rangle}$ states were examined systematically for rapid half-rotation of the magnetic field. It was verified that the phase shifts by $\ensuremath{\pi}$ rad in the adiabatic regime, but it does not shift from the original one in the nonadiabatic regime. These results support Robbins and Berry's claim [J. M. Robbins and M. V. Berry, J. Phys. A 27, L435 (1994)]. The fact that the interference fringes disappear in the intermediate regime and reappear in the nonadiabatic regime can be explained by the Majorana transition caused by a rapid reverse of the magnetic field.