  The interplay between coherent tunnel coupling and on-site interactions in
dissipation-free bosonic systems has lead to many spectacular observations,
ranging from the demonstration of number-phase uncertainty relation to quantum
phase transitions. To explore the effect of dissipation and coherent drive on
tunnel coupled interacting bosonic systems, we propose a device that is the
quantum optical analog of a Josephson interferometer. It consists of two
coherently driven linear optical cavities connected via a central cavity with a
single-photon nonlinearity. The Josephson-like oscillations in the light
emitted from the central cavity as a function of the phase difference between
two pumping fields can be suppressed by increasing the strength of the
nonlinear coupling. Remarkably, we find that in the limit of ultra-strong
interactions in the center-cavity, the coupled system maps on to an effective
Jaynes-Cummings system with a nonlinearity determined by the tunnel coupling
strength. In the limit of a single nonlinear cavity coupled to two linear
waveguides, the degree of photon antibunching from the nonlinear cavity
provides an excellent measure of the transition to the nonlinear regime where
Josephson oscillations are suppressed.
