  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.
