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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Geometrical manipulation of two-level atoms on the Bloch sphere observed in a time-domain atom interferometer

H. Imai, Y. Otsubo, Atsuo Morinaga

Published Jun 1, 2007• 0 citations
Publisher

Abstract

In this study, Berry's phases for various rotations of the Bloch vector were measured using a time-domain atom interferometer. Sodium atoms were cooled down less than 200 propK by the polarization gradient cooling and released from trap at almost zero magnetic field. Several geometrical manipulation of two-level atoms were demonstrated and examined.

DOI
10.1109/cleoe-iqec.2007.4386702

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Physical Review A•Feb 1, 1992•7 citations
In this study, Berry's phases for various rotations of the Bloch vector were measured using a time-domain atom interferometer. Sodium atoms were cooled down less than 200 propK by the polarization gradient cooling and released from trap at almost zero magnetic field. Several geometrical manipulation of two-level atoms were demonstrated and examined.
The geometric manipulation of the quantum states of two-level atoms with two laser-controlled resonant $\ensuremath{\pi}$ pulses with a relative phase difference was evaluated using a time-domain atom interferometer comprising a cold sodium atom ensemble and two copropagating two-photon Raman pulses. It was verified that the relative phase shift between two states is double the control phase difference and that the rotation around the axis 3 of the Bloch sphere can be controlled by geometric manipulation.
With carefully prepared resonant laser-controlled pulses, the two quantum states of a cold ensemble of sodium atoms were manipulated by pure geometric rotations of the Bloch vector around axes 2 and 3 on the Bloch sphere. The fidelity for two geometric rotations was improved to be 90%. A universal single-qubit operation on the ground-state wave function was demonstrated by a pure geometric operation and the phase shift due to the rotation around axis 3 was measured using a geometric atom interferometer.
We consider the geometrical phases arising in the state vector of two-level atoms due to their interaction with a self-consistently generated classical electrical field propagating without loss through the atomic medium. Three conservation laws are shown to exist generally and are used to solve for the individual quantum amplitudes, phases, and the electric field. We calculate the geometrical phases in two situations: (a) where the atoms are initially in the ground state and (b) where the initial state is a coherent superposition of the ground and excited states. In both cases the geometrical phase is the Aharonov-Anandan phase resulting from the atomic state vector tracing out a closed curve on the projective Hilbert space--here the Bloch sphere. We show that geometric quantities associated with the curve on the Bloch sphere are directly related to physical observables. The solid angle subtended by the closed curve (shown to equal twice the geometric phase) is a measure of the maximum atomic inversion, while the speed with which the curve is traced is related to the energy uncertainty in the state. An experimental method to observe the total phase change in a two-level subsystem is outlined, using photon echoes in a three-level medium.