Arturo Camacho, Rosario Paredes
The transition from Josephson oscillations to self-trapping regime in a system of three weakly coupled Bose-Einstein condensates in one dimension is investigated. We address the stationary and dynamical properties within both mean field and exact N-particle Bose-Hubbard schemes. Regarding the stationary properties we summarize the predictions of both approaches in a phase diagram as a function of interparticle interaction strength. From this analysis we identify the value of the critical interaction for which the transition occurs, and establish the limitations of the mean field against the Bose-Hubbard description, namely, that most of the stationary states are not accounted for by the former. Then, we characterize the dynamics and find that both schemes predict a continuous transition. By tracking the time evolution of the one-particle reduced density matrix in the N-particle Bose-Hubbard model we find the existence of stationary or equilibrium states, that appear as a consequence of intrinsic decoherence.
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http://arxiv.org/abs/1306.2650
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