Fluctuation-damping of isolated, oscillating Bose-Einstein condensates

Experiments on the nonequilibrium dynamics of an isolated Bose-Einstein condensate (BEC) in a magnetic double-well trap exhibit a puzzling divergence: While some show dissipation-free Josephson oscillations, others find strong damping. Such damping in isolated BECs cannot be understood on the level of the coherent Gross-Pitaevskii dynamics. Using the Keldysh functional-integral formalism, we describe the time-dependent system dynamics by means of a multi-mode BEC coupled to fluctuations (single-particle excitations) beyond the Gross-Pitaevskii saddle point. We find that the Josephson oscillations excite an excess of fluctuations when the effective Josephson frequency, ${\tilde{\omega }}_J$, is in resonance with the effective fluctuation energy, ${\tilde{\epsilon }}_m$, where both, ${\tilde{\omega }}_J$ and ${\tilde{\epsilon }}_m$, are strongly renormalized with respect to their noninteracting values. Evaluating and using the model parameters for the respective experiments describes quantitatively the presence or absence of damping.