Study On Cross-Kerr Effect And Nonreciprocal Amplification In Optomechanical Systems

An optomechanical system(OMS),which is one representative model to describe the interaction between the cavity intensity and the mechanical movement,is composed by a fixed mirror and a movable mirror that is coupled to the optical field in the cavity by radiation pressure.An optomechanical system is a good platform to study the coupling of optical and mechanical degrees of freedom.This system has potential applications in the fields of quantum mechanics,quantum optics and quantum information,such as optomechanical induced transparency,optomechanical induced amplification,quantum entanglement and quantum squeezing.Parity-time symmetry(PT symmetry)refers to the fact that a quantum system is kept unchanged under the parity-time transformations.This will help us to extend the study of quantum mechanics from the Hermitian form to the non-Hermitian one.Non-reciprocal amplification is a hot research area in recent years.By using optical interference effect,the signal transmission in a path can be enhanced,while the transmission in the reverse direction can be suppressed,so the signal amplification can be realized.In this paper,we mainly study the cross-Kerr effect in a PT symmetric optomechanical system and the optical nonreciprocal amplification in a three-mode optomechanical system.The main research contents are as follows:1.In the PT symmetric optomechanical system with cross Kerr effect,we have investigated the influence of cross-Kerr effect on the optomechanical induced transparency of the systemboth in the presence or absence of the PT symmetry.We find that the transformation from optomechanical induced transparency to optomechanical induced amplification can be realized by adjusting the nonlinear coupling or hopping coupling parameters,which provides a new scheme for us to effectively realize the optical switch from absorption to amplification.2.We have studied detailedly the phenomena of optical nonreciprocalamplification in a three-mode optomechanical system by exploring the effects of the relative phase,non-degenerate optical parametric coupling,and optomechanical coupling on the photon scattering probabilities.The three-mode optomechanical system can be derived effectively from the four-mode optomechanical system(two optical modes are cross-coupled with two mechanical modes)by using adiabatic elimination of the auxiliary mechanical mode.It is found that in the three-mode optical system,the optomechanical coupling and the non-degenerate optical coupling between the two optical modes will lead to nonreciprocal optomechanical amplification.