Abstract: This paper investigates a coupled cavity optomechanical system consisting of two Fabry-Pérot cavities and the two cavities are coupled via an optical fiber. Every cavity is made of one fixed mirror and a movable mirror, and the movable mirror can be regarded as a mechanical oscillators. Meanwhile, the two cavity modes are driven by classical laser fields. So, the interaction is inevitable between cavities, cavity and moving mirror, cavity and classical field. Firstly, in order to eliminate the two cavity fields, an effective Hamiltonian of the two phonon modes is derived by means of picture transformation, adiabatic eliminating, and rotating wave approximation ignoring the high frequency items, etc. Secondly, if the two mechanical oscillators initially are in coherent states, the coupled mechanical oscillators can be used to transmit state. Finally, in order to verify the analytical result, the fidelity of quantum state is numevically simulated, the result shows that the quantum state can be transferred periodically between the two mechanical oscillators, which is the same as the analytical result.

Key words: cavity optomechanical system, Hamiltonian, adiabatic eliminating, fidelity