Physical Review A

Phase shift of an adiabatic rotating magnetic field in Ramsey atom interferometry for m=0 sodium-atom spin states

Atsushi Takahashi, Hiromitsu Imai, 和也沼崎, Atsuo Morinaga

Published Nov 20, 2009• 8 citations

Abstract

The $\ensuremath{\pi}$-phase shift between $|F=1,{m}_{F}=0⟩$ and $|F=2,{m}_{F}=0⟩$ 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 $|1,0⟩$ and $|2,0⟩$ 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.

DOI: 10.1103/physreva.80.050102

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Physical Review A

Phase shift of an adiabatic rotating magnetic field in Ramsey atom interferometry for m=0 sodium-atom spin states

Atsushi Takahashi, Hiromitsu Imai, 和也沼崎, Atsuo Morinaga

Published Nov 20, 2009• 8 citations

Publisher

Abstract

The

\ensuremath{\pi}

-phase shift between

|F=1,{m}_{F}=0⟩

and

|F=2,{m}_{F}=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⟩

and

|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.

DOI: 10.1103/physreva.80.050102

Related papers

Interference fringes of m=0 spin states under the Majorana transition caused by rapid half-rotation of a magnetic field

Atsushi Takahashi, Atsuo Morinaga

The phase shift and visibility of fringes in the Ramsey atom interferometer composed of the $|F=1$ ,${m}_{F}=0\ensuremath{\rangle}$ and $|F=2$ ,${m}_{F}=0\ensuremath{\rangle}$ 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.The phase shift and visibility of fringes in the Ramsey atom interferometer composed of the $|F=1$,${m}_{F}=0\ensuremath{\rangle}$ and $|F=2$,${m}_{F}=0\ensuremath{\rangle}$ 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.

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The

\ensuremath{\pi}

-phase shift between

|F=1,{m}_{F}=0⟩

and

|F=2,{m}_{F}=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⟩

and

|2,0⟩

\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

,${m}_{F}=0\ensuremath{\rangle}$ and

|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.

Berry's phase of the atom in the state with a positive or negative

g

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

g

factor of the state.

g

factors. The solid angles for states with a positive

g

factor and with a negative

g

factor are verified to be $2\ensuremath{\pi}(1\ensuremath{-}\mathrm{cos}\ensuremath{\theta})$ and $\ensuremath{-}2\ensuremath{\pi}(1+\mathrm{cos}\ensuremath{\theta})$, respectively, for a right-handed rotation of a magnetic field and a semiangle of $0\ensuremath{\leqslant}\ensuremath{\theta}\ensuremath{\leqslant}\ensuremath{\pi}/2$.