  The rapid progress in quantum technology enables the implementation of
artificial many-body systems with correlated photons and polaritons. A
multiconnected Jaynes-Cummings (MCJC) lattice can be constructed by connecting
qubits and cavities alternatively. Such kind of models can be realized with
superconducting qubits coupled to superconducting microwave resonators or with
quantum dots coupled to optical nanocavities. We study physical properties of
the one-dimensional MCJC lattice using the density-matrix renormalization group
method. This model has an intrinsic symmetry between the left and right
qubit-cavity couplings. The competition between these couplings may drive the
ground state either to a Mott-insulating or to a superfluid phase at an integer
filling. We calculate the single-particle and density-density correlation
functions, the correlation lengths in the Mott-insulating phase and the
Luttinger parameters in the superfluid phase, and determine accurately the
critical points that separate these two phases.
