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 intercavity tunnel coupling, the nonequilibrium 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 transmission spectrum of the system, as well as in the intensity correlations of the transmitted light. Possible experimental implementations in state-of-the-art solid-state devices are discussed.