Dissipative dynamics of Bose condensates in optical cavities

We study the zero-temperature dynamics of Bose-Einstein condensates in driven high-quality optical cavities in the limit of large atom-field detuning in a one-dimensional model. We calculate the stationary ground state and the spectrum of coupled atom and field mode excitations for standing-wave cavities as well as for traveling-wave cavities. Finite cavity response times lead to damping or controlled amplification of these excitations. Analytic solutions in the Lamb-Dicke expansion are in good agreement with numerical results for the full problem and show that oscillation frequencies and the corresponding damping rates are qualitatively different for the two cases.