Nonlinear and chaotic dynamics of a Bose-Einstein condensate in an optical cavity

We present a theoretical analysis of a Bose-Einstein condensate (BEC) enclosed in an optical cavity driven by an external laser beam. In the limit where the cavity-field dynamics is adiabatically eliminated, the interaction between the condensate and the cavity displays a range of nonlinear dynamical behaviors such as multistability, quasiperiodicity, and conservative chaotic oscillations. We show that chaotic oscillations are ubiquitous when repulsive atom-atom interactions are included in the model. Despite the complexity of the full coupled BEC-cavity system, the essential features of its nonlinear and chaotic behavior are low-dimensional and are well described by considering the evolution of only a few motional states of the BEC.