  We investigate two coupled nonlinear cavities that are coherently driven in a
dissipative environment. We perform semiclassical, numerical and analytical
quantum studies of this dimer model when both cavities are symmetrically
driven. In the semiclassical analysis, we find steady-state solutions with
different photon occupations in two cavities. Such states can be considered
analogs of the closed system double well symmetry breaking states. We analyze
the occurrence and properties of these localized states in the system parameter
space and examine how the symmetry breaking states, in form of a bistable pair,
are associated to the single cavity bistable behavior. In a full quantum
calculation of the master equation dynamics that includes quantum fluctuations,
the symmetry breaking states and bistability disappear due to the quantum
fluctuations. In quantum trajectory picture, we observe enhanced quantum jumps
and switching which indicate the presence of the underlying semiclassical
symmetry breaking states. Finally, we present a set of analytical solutions for
the steady state correlation functions using the complex P-representation and
discuss its regime of validity.
