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, ω̃J, is in resonance with the effective fluctuation energy, ε̃m, where both, ω̃J and ε̃m, 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.