Quantum phase transitions for two coupled sites with dipole-coupled   effective Jaynes-Cummings model
  The nature of the ground states for a system composed of two coupled cavities with each containing a pair of dipole-coupled two-level atoms are studied over a wide range of detunings and dipole coupling strengths. The cases for three limits of exact resonance, large positive and negative detunings are discussed, and four types of the ground states are revealed. Then the phase diagrams of the ground state are plotted by choosing three different "order parameters". We find that the phase space, determined by the combinative action of detuning and the dipole coupling strength, is divided into four regions. This is different from the general Bose-Hubbard model and more richer physics are presented in the two-site coupled cavities system. That is, the insulator region may be polaritonic or atomic and the superfluid region may be polaritonic or photonic in nature. 
Lei Tan, Yu Qing Zhang, Wu Ming Liu
quant-ph