Quantum dynamics of a couple cavity opto-mechanical system: Three mode & four mode entanglement

Abstract We explore the possibilities of intermodal entanglement for couple cavity optomechanical system. The Hamiltonian of the system is solved analytically and solutions are obtained neglecting effect of dissipation and driving, for both the cavity field modes and mechanical modes. The occurrence of three mode and four mode entanglement are investigated by using Li. et al. criterion. Temporal variations of these nonclassical properties are studied for different phase angle of the cavity field modes and dependence on photon hopping interaction term, coupling strength are also reported. To account for cavity loss, mechanical damping and presence of driving, a numerical solution using a master equation approach is done. Entangled state between two mechanical modes is observed i.e. at macroscopic scale.