Strong Coupling Theory for the Jaynes-Cummings-Hubbard Model

We present an analytic strong-coupling approach to the phase diagram and elementary excitations of the Jaynes-Cummings-Hubbard model describing a superfluid-insulator transition of polaritons in an array of coupled QED cavities. In the Mott phase, we find four modes corresponding to particle or hole excitations with lower and upper polaritons, respectively. Simple formulas are derived for the dispersion and spectral weights within a strong-coupling random-phase approximation (RPA). The phase boundary is calculated beyond RPA by including the leading correction due to quantum fluctuations.