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arXiv:0811.2139 · Annals of Physics

Coherent state approach to the cross-collisional effects in the population dynamics of a two-mode Bose–Einstein condensate

Thiago F. Viscondi, K. Furuya, M.C. de Oliveira

Published Jun 4, 2009• 9 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2009.05.008

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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.
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We investigate the coherence dynamics of a two-mode Bose-Einstein condensate coupled with the environment in the mean-field approximation. We give an analytical result of the time-average coherence in the absence of system-environment coupling, and find that the time-average coherence attains its maximum value at the critical point which corresponds to the boundary between the self-trapping regime and the Josephson oscillation regime. The effect of noise on dynamical coherence is also considered by analyzing the couplings of the condensate to the environment. With the first kind of coupling, the coherence finally stabilizes at a fixed value. Meanwhile, we show that the presence of the noise can even enhance the coherence for some particular interaction. With the second kind of coupling as collisional dephasing, the noise leads a sudden transition of the coherence which then subjects to an exponential decay.