Two-photon Rabi-Hubbard and Jaynes-Cummings-Hubbard models: Photon-pair superradiance, Mott insulator, and normal phases

We study the ground-state phase diagrams of two-photon Dicke, one-dimensional Jaynes-Cummings-Hubbard (JCH), and Rabi-Hubbard (RH) models using mean-field, perturbation, quantum Monte Carlo (QMC), and density-matrix renormalization-group methods. We first compare mean-field predictions for the phase diagram of the Dicke model with exact QMC results and find excellent agreement. The phase diagram of the JCH model is then shown to exhibit a single Mott insulator lobe with two excitons per site, a superfluid (SF, superradiant) phase and a large region of instability where the Hamiltonian becomes unbounded. Unlike the one-photon model, there are no higher Mott lobes. Also, unlike the one-photon case, the SF phases above and below the Mott lobe are surprisingly different: Below the Mott lobe, the SF consists of photon pairs as opposed to above the Mott lobe, where it is SF of simple photons. The mean-field phase diagram of the RH model predicts a transition from a normal to a superradiant phase but none is found with QMC.