Fermionized photons in one-dimensional coupled cavities

We consider the properties of a one-dimensional array of evanescently coupled high-finesse cavities each containing a single neutral atom, in the limit of low photon densities. The ground state of the corresponding Jaynes-Cummings-Hubbard (JCH) model is obtained numerically using the Density Matrix Renormalization Group algorithm. We find strong evidence for the existence of a Tonks-Girardeau phase, in which the photons are strongly fermionized, between the Mott-insulating and superfluid phases as a function of the inter-cavity coupling. Results for photon and spin excitation densities, one- and two-body correlation functions, and superfluid and condensate fractions are all found to be consistent with this conclusion.