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. We calculate the stationary ground state and the spectrum of coupled atom and field mode excitations for standing wave cavities as well as for travelling 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.