Excitations of strongly correlated lattice polaritons.

We present an analytic slave-boson approach to calculate the elementary excitations of the Jaynes-Cummings-Hubbard model (JCHM) describing strongly correlated polaritons on a lattice in various quantum optical systems. In the superfluid phase near the Mott transition we find a gapless, linear Goldstone mode and a gapped amplitude mode corresponding to phase and density fluctuations, respectively. The sound velocity of the Goldstone mode develops a peculiar anomaly as a function of detuning at low densities, which persists into the weakly interacting regime of a polariton BEC.