  The connectivity and tunability of superconducting qubits and resonators
provide us with an appealing platform to study the many-body physics of
microwave excitations. Here we present a multi-connected Jaynes-Cummings
lattice model which is symmetric with respect to the nonlocal qubit-resonator
couplings. Our calculation shows that this model exhibits a Mott
insulator-superfluid-Mott insulator phase transition, featured by a reentry to
the Mott insulator phase, at commensurate filling. The phase diagrams in the
grand canonical ensemble are also derived, which confirm the incompressibility
of the Mott insulator phase. Different from a general-purposed quantum
computer, it only requires two operations to demonstrate this phase transition:
the preparation and the detection of the commensurate many-body ground state.
We discuss the realization of these operations in a superconducting circuit.
