Entanglement And Squeezing In A Two-mechanical-mode Optomechanical System With Kerr-down-conversion Crystal

It is found that optomechanical system(OMS) has many important applications in quantum optics and information science. Recently, the research on OMS has achieved rapid development, such as optomechanically induced transparency(OMIT) etc.. In recent years, OMS has attracted a great interest due to its wide application, especially, in the quantum entanglement, squeezing properties and the nonlinear behavior induced by the nonlinear crystal in the optomechanical system. In this paper, we shall investigate the nonlinear dynamic behavior in a two-mechanical-mode optomechanical system with the Kerr-down-conversion crystal composed by a Kerr medium and a degenerate optical parametric amplitude(OPA).We study the effects of the Kerr medium and OPA on the entanglement between the two movable mirrors and the squeezing spectra in an optomechanical system. The paper is organized as follows:In Chap. I, we introduce the optomechanical system, and its properties of the entanglement and squeezing, as well as its nonlinear features with nonlinear media.In Chap. II, we shall investigate the nonlinear features of a two-mechanical-mode optomechanical system with the Kerr-down-conversion crystal(Kerr medium and OPA) by calculating the output spectra.In Chap. III, we shall study the effects of the nonlinear media and the environment temperature on the squeezing of the output field in the two-mechanical-mode optomechanical system with the Kerr-down-conversion crystal.In Chap. IV, we shall investigate the entanglement between two mechanical modes in the optomechanical cavity with the Kerr-down-conversion crystal, and discuss the effects of the nonlinear crystal on the entanglement.In Chap. V, we summarize our main results of this paper and display the outlook.