Atomic entanglement versus visibility of photon interference for quantum criticality of a hybrid system

We use the two-atom concurrence and the visibility of interference fringes of photons to characterize a quantum phase transition for a hybrid system consisting of an array of coupled cavities and each cavity doped with a two-level atom. We compare them with the total excitation number fluctuation. Analytical and numerical simulation results show quantum critical phenomena similar to the Mott insulator to superfluid transition. Here, the contour lines of the atomic concurrence, the visibility of interference fringes of photons, and the excitation number fluctuation in the phase diagram are consistent in the vicinity of the nonanalytic locus of the atomic concurrence.