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Chinese Physics Letters

Dynamical and Geometric Phases of a Two Energy-Level Bose–Einstein Condensate Interacting with a Laser Field

Zhao-Xian Yu, Jiao Zhi-Yong, Shuo Jin, Ji‐Suo Wang

Published Jan 18, 2007• 1 citation
Publisher

Abstract

By using of the invariant theory, we study a two energy-level Bose–Einstein condensate interacting with a time-dependent laser field, the dynamical and geometric phases are given respectively. The Aharonov–Anandan phase is also obtained under the cyclical evolution.
DOI
10.1088/0256-307x/24/2/008

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In terms of exact solutions of the time-dependent Schr\"odinger equation for an effective giant spin modeled from a coupled two-mode Bose-Einstein condensate (BEC) with adiabatic and cyclic time-varying Raman coupling between two hyperfine states of the BEC, we obtain analytic time-evolution formulas of the population imbalance and relative phase between two components with various initial states, especially the SU(2) coherent state. We find the Berry phase depending on the number parity of atoms, and particle number dependence of the collapse revival of population-imbalance oscillation. It is shown that self-trapping and phase locking can be achieved from initial SU(2) coherent states with proper parameters.