Trimeric Chain of Bose-Einstein Condensates: Parameter Dependence and Chaos Onset
Francesco Buonsante
Abstract
We report an extensive analysis of the dynamics of three interacting Bose-Einstein condensates arranged into a row, where both the depth of the central well, $w$, and the interwell tunneling rate, $T$, are regarded as adjustable parameters. The interest of such a system, whose impending experimental realization is promised by the striking technical progress achieved in the field of BEC in the last few years, lies in the fact that it is still sufficiently simple to allow an entirely analytical approach, yet at the same time it exhibits such complexity to deter from merging it in the same class as the dimer. The system is described in the mean-field limit, which, being essentially equivalent to the Bogoliubov approximation, is expected to give a satisfactory picture when the average well population is large. In this limit, where the dimer dynamics is known to be integrable, we systematically identify the configuration and the stability character of the fixed points of the trimer dynamics as functions of the Hamiltonian parameters $T$ and $w$. Such analytical results are widely confirmed by numerical simulations where the chaoticity of the unstable fixed points is manifest. Based on our analysis we point out and discuss some interesting features of the system which, owing to their macroscopic character, seem viable to experimental test.
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