Coupled Cavity Array System In The Mott Insulating To The Superfluid Phase Transition

We have studied the characterization and detection of the Mott insulator to superfluid phase transition in the coupled cavity array systems. For the hybrid system consisting of an array of coupled cavities and each cavity doped with a two-level atom, we use the two-atom concurrence and the visibility of interference fringes of photons to compare with the total excitation number fluctuation. Analytical and numerical simulation results show that these three quantities could be employed to character the Mott insulator to superfluid transition. For the system with that each cavity contains a few atoms and different cavities may have different atom numbers, it is found that even for small systems, although the number of two-level atoms is very small, the fluctuation of the atom number between adjacent cavities will induce the fluctuation of the repulsive interaction, and accordingly the coexistence of the Mott insulator state, the superfluid state and the third state, where photons collect in the cavity with more atoms. Meanwhile, the two-atom concurrence and visibility of interference fringes of photons also exhibit some new features. For the construction and detection of the phase diagram of the Mott insulator to superfluid transition in finite systems, numerical results show that, through introducing a weakly connected external system, the Josephson current between two systems is proportional to the superfluid order parameter of the finite system, which is obtained by introducing an external field. Numerical simulations show that the profile of the obtained Mott lobes is analogous to that of the Mott lobes usually obtained by the mean field approach, which opens up a possibility to detect the Bose-Einstein condensates in small quantum devices.