Frozen photons in Jaynes Cummings arrays

We study the origin of "frozen" states in coupled Jaynes-Cummings-Hubbard arrays in the presence of losses. For the case of half the array initially populated with photons while the other half is left empty we show the emergence of self-localized photon or "frozen" states for specific values of the local atom-photon coupling. We analyze the dynamics in the quantum regime and discover important additional features appear not captured by a semiclassical treatment, which we analyze for different array sizes and filling fractions. We trace the origin of this interaction-induced photon "freezing" to the suppression of excitation of propagating modes in the system at large interaction strengths. We discuss in detail the possibility to experimentally probe the relevant transition by analyzing the emitted photon correlations. We find a strong signature of the effect in the emitted photons statistics.