Alexandre B. Tacla, Carlton M. Caves
We study the mean-field dynamics and the reduced-dimension character of two-mode Bose-Einstein condensates (BECs) in highly anisotropic traps. By means of perturbative techniques, we show that the tightly-confined (transverse) degrees of freedom can be decoupled from the time evolution equations at the expense of introducing additional effective three-body, attractive, intra- and interspecies interactions. These interactions are mediated by changes in the transverse wave function. This perturbation theory is valid as long as the nonlinear scattering energy is small compared to the transverse energy scales. This approach leads to reduced-dimension mean-field equations that optimally describe the evolution of the two-mode condensate in general quasi-1D and quasi-2D geometries. We use this model to investigate the relative phase and density dynamics of a two-mode, cigar-shaped $^{87}$Rb BEC. We study the relative phase dynamics in the context of a nonlinear Ramsey interferometry scheme, which has recently been proposed as a novel platform for high-precision interferometry. Numerical integration of the coupled, time-dependent, three-dimensional, two-mode Gross-Pitaevskii equations for various atom numbers shows that this model gives a considerably more refined analytical account of the mean-field evolution than an idealized quasi-1D description.
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http://arxiv.org/abs/1207.3817
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