An array of coupled cavities, each of which contains an N four-level atom, is investigated. When cavity fields dispersively interact with the atoms, an effective Bose-Hubbard model can be achieved. By numerically comparing the full Hamiltonian with the effective one, we find that within the parameters region, the effective Hamiltonian can completely account for the Mott-insulator as well as the phase transition from the similar Mott-insulator to superfluid. Through jointly adjusting the classical Rabi frequency and the detuning, the nonlinearity can be improved.

A single four-level atom interacting with two-mode cavities is investigated. Under large detuning condition, we obtain the effective Hamiltonian which is unitary squeezing operator of two-mode fields. Employing the input-output theory, we find that the entanglement and squeezing of the output fields can be achieved. By analyzing the squeezing spectrum, we show that asymmetric detuning and asymmetric atomic initial state split the squeezing spectrum from one valley into two minimum values, and appropriate leakage of the cavity is needed for obtaining output entangled fields.

We study the system consisting of a one-dimension waveguide side-coupled to a nonlinear cavity which was doped with a lambda-type atom and investigate the control of photons transport in one-dimension waveguide through manipulating the atom contained in the cavity. Employing the polariton technique, we show that in the single-photon case, the system behaves as a waveguide coupled to a two-level system. By solving the Schrödinger equation, we show that single photon switch can be achieved by tuning the Rabi frequency of the classical field. In the two-photon case, the system behaves like a waveguide coupled to a cascade three-level system. Two-photon quantum correlation in the position variation can be controlled by adjusting the Rabi frequency.