Phase Diagram of A Multi-connected Superconducting Jaynes-Cummings Lattice at Commensurate and Incommensurate Fillings

A multi-connected superconducting Jaynes-Cummings lattice can be constructed with alternatively-connected superconducting qubits and resonators. In a one-dimensional configuration, this model bears an intrinsic symmetry between the left and the right qubit-resonator couplings. Here we study the quantum phase transition of this model using the exact diagonalization method. At commensurate fillings, the off-diagonal long range order of the single-particle density matrix and the energy gap are calculated. We obtain the phase diagram of this model, which demonstrates a symmetry between the couplings and a reentry to the Mott insulator phase. For a system with given chemical potential, the density of the excitations contains integer-valued plateaus between critical chemical potentials that define the boundaries of different many-body phases and indicate the phase transition. We also discuss the implementation of this model with superconducting devices, including the state preparation and detection schemes. \\[0pt] [1] K. Seo and L. Tian, eprint arXiv:1408.2304.