Quantum phase diagrams of the Jaynes–Cummings Hubbard models in non-rectangular lattices

In this paper, we investigate systematically the quantum phase transition between the Mott-insulator and superfluid states of the Jaynes–Cummings Hubbard model in triangular, square, honeycomb and kagomé lattices. With the help of Green's function method, by treating the hopping term in the Jaynes–Cummings Hubbard model as perturbation, we calculate the phase boundaries of Jaynes–Cummings Hubbard models on different geometrical lattices analytically up to second order for both detuning $\Delta =0$ and $\Delta \ne 0$. It is shown that the Mott phase becomes more unstable when increasing the polariton number n. Meanwhile, the Mott lobe of n  =  0 is enlarged while other Mott lobes shrink as the detuning parameter $\Delta$ increases. (paper)