  We introduce and study the properties of an array of QED cavities coupled by
nonlinear elements, in the presence of photon leakage and driven by a coherent
source. The nonlinear couplings lead to photon hopping and to nearest-neighbor
Kerr terms. By tuning the system parameters, the steady state of the array can
exhibit a photon crystal associated with a periodic modulation of the photon
blockade. In some cases, the crystalline ordering may coexist with phase
synchronization. The class of cavity arrays we consider can be built with
superconducting circuits of existing technology.
