We discuss analytic approximations to the ground-state phase diagram of the homogeneous Jaynes-Cummings-Hubbard (JCH) Hamiltonian with general short-range hopping. The JCH model describes, e.g., radial phonon excitations of a linear chain of ions coupled to an external laser field tuned to the red motional sideband with Coulomb-mediated hopping or an array of high-
Q coupled cavities containing a two-level atom and photons. Specifically, we consider the cases of a linear array of coupled cavities and a linear ion chain. We derive approximate analytic expressions for the boundaries between Mott-insulating and superfluid phases and give explicit expressions for the critical value of the hopping amplitude within the different approximation schemes. In the case of an array of cavities, which is represented by the standard JCH model, we compare both approximations to numerical data from density-matrix renormalization-group calculations.
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 and . 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 increases.