Role of quantum fluctuations in the optomechanical properties of a Bose-Einstein condensate in a ring cavity

We analyze a detailed model of a Bose-Einstein condensate (BEC) trapped in a ring optical resonator and contrast its classical and quantum properties to those of a Fabry-Pérot geometry. The inclusion of two counterpropagating light fields and three matter field modes leads to important differences between the two situations. Specifically, we identify an experimentally realizable region where the system's behavior differs strongly from that of a BEC in a Fabry-Pérot cavity, and also where quantum corrections become significant. The classical dynamics are rich, and near bifurcation points in the mean-field classical system, the quantum fluctuations have a major impact on the system's dynamics.