Fluorescence spectrum of thermally driven array of QED cavities

Developments in cavity QED technology allow us to engineer strong interactions between photons and atoms and therefore create possibilities to use light-matter systems as quantum simulators of many-body quantum systems. Quantum Phase Transition (QPT) of photons in arrays of coupled cavities described by models of closed systems such as the Jaynes-Cummings-Hubbard and the Rabi-Hubbard models (RHM) [1-8] have been studied extensively during last few years [1-8]. Our aim is to describe more realistic situations in which the system is open to an environment. We consider the RHM in which photons can leak out of the cavities. Based on the generalized input-output formalism, we show that measuring the fluorescence spectrum of the leaked photons gives us information about the system and the nature of the QPT.\\[4pt] [1] A. D. Greentree et al., Nature Phys. {\bf 466}, 856 (2006)\\[0pt] [2] M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, Nature Phys. {\bf 462}, 849 (2006).\\[0pt] [3] A. Tomadin, V. Giovannetti, R. Fazio, D. Gerace, I. Carusotto, Hakan E. T\"ureci, A. Imamoglu Phys. Rev. A {\bf 81}, 061801(R) (2010).\\[0pt] [4] S. Schmidt and G. Blatter Phys. Rev. Lett. {\bf 103}, 086493 (2009).