Theoretical Studies On Entanglement And Electromagnetically Induced Transparency In Cavity Optomechanical System

A representative optomechanical system is composed of an optical resonator and a nanomechanical oscillator, which makes optical degrees of freedom couple with mechani-cal degrees of freedom, and mutually modulates the cavity field and mechanical oscillator each other. Under some certain conditions, the quantum properties of the cavity field can be reflected by the mesoscopic mechanical oscillator, and thus the observation and study of the quantum behaviors of the macroscopic objects can be realized. Therefore, the research of optomechanical system has very important significance on the research of basic quan-tum mechanics, quantum communication and the precision detection of optical signals, etc. Meanwhile, a significant advantage of the optomechanical system is the fact that the optical resonator provides a good platform for the interaction between matter and optical cavity field, which makes some auxiliary system represented by atom, electron and quantum dot introduced into the optomechanical system easily. The participation of atomic media is con-sidered to effectively enhancing the nonlinear coupling between cavity field and mechanical oscillator, which is benefit for studying the quantum effects of the optomechanical system, such as electromagnetically induced transparent (EIT), the preparation of the entanglement state and squeezed state of the mechanical oscillator, etc.In this thesis, we focus on the phenomenon of quantum entanglement and EIT in the optomechanical system coupled with atom. Employing the quantum Langevin equations and input-output relation of the cavity, we propose a theoretical scheme preparing multipartite entanglement state by using a single four-level atom to couple two cavity mode. The single four-level atom driven by classical laser induced the entanglement between the two movable mirrors, the two-mode fields, and also the mirror and the distant cavity mode. Meanwhile, the energy difference between the two lowest levels of the four-level atom is not negligible, the mesoscopic entanglement of the mirrors as well as the squeezing spectrum of the output cavity fields display a splitting phenomenon. Optomechanical system coupled with atoms can not only produce mesoscopic entanglement, but also show multiple-EIT. We study the multiple-EIT which is caused by two-level atomic media couple to a ring optomechanical cavity with a fixed mirror and two movable mirrors, and we discuss how the decay rate of the atoms affect the number and the width of the transparent windows. Moreover, we investigate the response of the output field of multiple mechanical modes coupled to a single quantized cavity field via quadratic optomechanical interactions. The result shows that the multiple-EIT in our paper can be observed even for the membranes with same frequencies.The research in this thesis is helpful for understanding the nonlinear optical effects in hybrid optomechanical systems. So it has some positive effect and certain reference value on the research of the nonlinear optical system for precision measurement.