Photonic Josephson effect, phase transitions, and chaos in optomechanical systems

A photonic analog of the Josephson effect is analyzed for a system formed by a partly transparent mechanical membrane dividing an optical cavity into two halves. Photons tunneling between the two sub-cavities constitute the coherent Jospehson current. The force acting upon the membrane due to the light pressure induces a nonlinearity which results in a rich dynamical structure. For example, contrary to standard bosonic Josephson systems, we encounter chaos. By means of a mean-field approach we identify the various regimes and corresponding phase diagram. At the short time scale, chaos is demonstrated to prevent regular self-trapping, while for longer times a dissipation induced self-trapping effect is possible.