  We study a coupled array of coherently driven photonic cavities, which maps
onto a driven-dissipative XY spin-$\frac{1}{2}$ model with ferromagnetic
couplings in the limit of strong optical nonlinearities. Using a site-decoupled
mean-field approximation, we identify steady state phases with canted
antiferromagnetic order, in addition to limit cycle phases, where oscillatory
dynamics persist indefinitely. We also identify collective bistable phases,
where the system supports two steady states among spatially uniform,
antiferromagnetic, and limit cycle phases. We compare these mean-field results
to exact quantum trajectories simulations for finite one-dimensional arrays.
The exact results exhibit short-range antiferromagnetic order for parameters
that have significant overlap with the mean-field phase diagram. In the
mean-field bistable regime, the exact quantum dynamics exhibits real-time
collective switching between macroscopically distinguishable states. We present
a clear physical picture for this dynamics, and establish a simple relationship
between the switching times and properties of the quantum Liouvillian.
