Nonlinear atom-field dynamics in high-Q cavities: from a BEC to a thermal gas

A cold gas of polarizable particles moving in the optical potential of a standing wave high finesse optical resonator acts as a dynamic refractive index. For a sufficiently strong cavity pump the optical forces generated by the intra cavity field perturb the particles phase space distribution, which shifts the optical resonance frequency and induces a nonlinear optical response. By help of the corresponding Vlasov equation we predict that beyond the known phenomenon of optical bi-stability one finds regions in parameter space, where no stable stationary solution exists. The atom field dynamics then exhibits oscillatory solutions converging to stable limit cycles of the system. The linearized analytical predictions agree well with corresponding numerical solutions of the full time dependent equations and first experimental observation in both cases.