T. P. Billam, P. Mason, S. A. Gardiner
While the Gross-Pitaevskii equation is well-established as the canonical dynamical description of atomic Bose-Einstein condensates at zero-temperature, describing the dynamics of Bose-Einstein condensates at finite temperatures remains a difficult theoretical problem, particularly when considering low-temperature, non-equilibrium systems in which depletion of the condensate occurs dynamically as a result of external driving. The BEC analog of the quantum delta-kicked rotor is the prototypical example of such a system. In this paper, we describe a fully time-dependent numerical method to propagate the equations of motion of a second-order, number-conserving description; these equations describe the coupled dynamics of the condensate and non-condensate fractions in a self-consistent manner, and correctly capture the phonon-like nature of excitations at low temperature, making them ideal for the study of low-temperature, non-equilibrium, driven systems. We use this numerical method to systematically explore the finite-temperature dynamics of the delta-kicked-rotor-BEC. We demonstrate that several qualitative features of this system at zero temperature are well-preserved at finite temperatures, and predict a finite-temperature shift of resonance frequencies which could be verified by future experiments.
View original:
http://arxiv.org/abs/1207.2821
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