Mott insulating and glassy phases of polaritons in arrays of coupled cavities

By means of analytical and numerical methods we analyze the phase diagram of polaritons in onedimensional coupled cavities. We locate the phase boundary, discuss the behavior of the polariton compressibility and visibility fringes across the critical point, and find a nontrivial scaling of the phase boundary as a function of the number of atoms inside each cavity. We also predict the emergence of a polaritonic glassy phase when the number of atoms fluctuates from cavity to cavity.