Fermionized photons in an array of driven dissipative nonlinear cavities

We theoretically investigate the optical response of a one-dimensional array of strongly nonlinear optical microcavities. When the optical nonlinearity is much larger than both losses and inter-cavity tunnel coupling, the non-equilibrium steady state of the system is reminiscent of a strongly correlated Tonks-Girardeau gas of impenetrable bosons. Signatures of strong correlations are identified in the absorption spectrum of the system, as well as in the intensity correlations of the emitted light. Possible experimental implementations in state-of-the-art solid-state devices are discussed.