Continuous variable entanglement generation in coupled cavities

We investigate continuous variable entanglement produced in two distant coupled cavities, in which two four-level atoms are driven by classical fields respectively. Under the large detuning condition, an effective Hamiltonian containing the square of creation (annihilation) operator of cavity field is derived. Due to the nonlinearity, entanglement formally created by the beam splitter type interaction is transformed into the nondegenerate parametric down conversion type. Employing the operator algebraic method, we study the time evolution of entanglement condition, and show that the system provides us advantage in achieving a larger photon number with better entanglement. We also discuss the dissipation of the cavities affecting the entanglement.