Macroscopic entanglement in optomechanical system induced by non-Markovian environment

In this paper, the non-Markovian dynamics of an optomechanical system is analyzed by using the non-Markovian quantum state diffusion (NMQSD) method. An exact solution is obtained for the system composed of a Fabry-Pérot (F-P) cavity with two movable mirrors without the linearization of the Hamiltonian. Based on the solution, we find that the memory effect of the non-Markovian environment can be used to generate macroscopic entanglement between two mirrors. In order to achieve the maximum entanglement generation, the non-Markovian properties of the environment have to be chosen carefully depending on the properties of the system. Then, we also show that the coherence (superposition) in the initial state may produce entanglement in the evolution. At last, we show the entanglement sudden death and revival significantly depend on the strength of the memory effect, and the entanglement revival can be only observed in non-Markovian case. Our treatment, as an example, paves a way to exactly solve a large category of optomechanical systems without the linearization of the Hamiltonian.