Collective Dynamics of Bose-Einstein Condensates in Optical Cavities

Experiments on Bose-Einstein condensates in optical cavities have observed a coherent state of the matter-light system-superradiance. The nature of these experiments demands consideration of collective dynamics. Including cavity leakage and the backreaction of the cavity field on the condensate, we find a rich phase diagram including multiphase coexistence regions, and persistent optomechanical oscillations. The proximity of the phase boundaries results in a critical slowing down of the decay of many-body oscillations, which can be enhanced by large cavity loss.