Quantum Phase Transition in A Multi-connected Superconducting Jaynes-Cummings Lattice

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 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 the superconducting circuit