Quantum Phase Transition of Light in the Rabi-Hubbard Model

We discuss the physics of the Rabi-Hubbard model describing large arrays of coupled cavities interacting with two level atoms via a Rabi non-linearity. We show that the inclusion of counter-rotating terms in the light-matter interaction, often neglected in theoretical descriptions based on Jaynes-Cumming models, is crucial to stabilize finite-density quantum phases of correlated photons with no need for an artificially engineered chemical potential. We show that the physical properties of these phases and the quantum phase transition occurring between them is remarkably different from those of interacting bosonic massive quantum particles. The competition between photon delocalization and Rabi non-linearity drives the system across a novel $Z_2$ parity symmetry-breaking quantum phase transition between two gapped phases, a Rabi insulator and a delocalized super-radiant phase.