Theoretical Study Of The Quantum Properties In Cavity Optomechanical System

In recent years, the cavity optomechanical system is undergoing rapid development, and becomes a hot topic of the widespread attention in theory and experiment. A typical cavity optomechanical system is composed of an optical cavity and a nanomechanical oscillator. In this system, the radiation pressure in a cavity field exerts a force on the mechanical oscillator, which moves freely near the eigenfrequency. Conversely, the mechanical vibrations modu-lates the cavity field frequency. Cavity optomechanical systems are the nanoscale mechanical systems with ultra-high mechanical quality factor, the ultra-high frequency, the ultra-low effective mass, the ultra-high sensitivity. This system can be used to detect the force and displacement. If the cavity optomechanical system is coupled to other quantum systems(such as atoms, electrons, quantum dots, etc.), which may be used to detect quantum phenomena and a fundamental quantum law. For instance, a precise measurement of the atomic emis-sion spectrum, laser trapping technology, the control of ultra-cold atom, and the detecting of the force generated by a single atom. The interaction of mechanical degrees of freedom and optical cavity by means of radiation pressure is undergoing a paradigm shift in control and measurement of mechanical motion. Radiation pressure coupling has opened an broad area of possibilities, both applied and fundamental. With the sustained trends toward miniatur-ization and dissipation reduction, which will provide a way to probe the quantum regime of detection of micro-mechanical oscillator both in terms of technology or in the basic sciences, and cause entirely new ways of controlling mechanics and photon. It also seems likely that beyond precision measurement, there will be new technologies for controlling cooling and am-plification. Simultaneously, the realization of quantum cavity optomechanical system control has a great application value in the area of the quantum information processing.In this thesis, we choose cavity optomechanical systems as the research object, then dis-cuss the photon tunneling, the detection for the displacement and frequency of the dielectric membrane, and the detecting of the atomic emission spectrum and cavity field spectrum. It achieves photon-phonon conversion by adjusting the spectra intensity and offers a novel perspective for the entangled state preparation and quantum information transfer, quantum communication. This thesis is divided into five chapters, where the third to the fifth chapters are our main research work, the specific content is organized as follows: In Chapter one, we give a brief introduction to the research background, the present situation and application of the cavity optomechanical systems, introduce several typical cavity optomechanical system models and the repaired experimental parameter. Finally, the main work of this thesis and the arrangement of the chapters is given.In Chapter two, we briefly describe some basic principle of the cavity optomechanical systems and the basic knowledge of quantum mechanics, including the input-output theory, the brownian motion of the mechanical oscillator, the cigenmode and the classical theory of the radiation pressure, and the optical bistability. Finally, we present briefly the quantum basic knowledge, which includes the nonlinear quantum Langevin equation, the mean-field approximation and the time-dependent physical spectrum of light.In Chapter three, we mainly discuss the photon inversion and the mechanical membrane position of a membrane inside a cavity. First, in the quantum regime, we study the quantum properties of the photon inversion in different experimental parameters and the initial state of the system by numerical simulation method. In addition, by the master equation for an open system, we obtain a nonlinear equations in the mean-field approximation, and discuss the quantum correlation between the photon inversion and the mechanical membrane position. Meanwhile, we achieve the control of the mechanical frequency and displacement by means of regulating photons number in cavity optomechanics. In addition, the decoherence effects of the systems are taken into account.In Chapter four, we discuss that a Fabry-Perot cavity coupled to a two-level atom, and research the effect of the different experimental parameters, the coupling strength and the number of photons and phonons on the atomic emission spectrum under different initial state of the system. Further, in the case of weak optomechanical coupling, we obtain approx-imativcly the analytical solution of the atomic emission spectrum by Taylor series expansion method, and explain the difference between analytical solutions and numerical simulations for the atomic emission spectrum. Finally, we discuss the effects of the nonlinear Kcrr medium on the atomic emission spectrum in the optomechanical cavity with a nonlinear Kcrr medium.In Chapter five, we consider a optomechanical system with a nonlinear Kcrr medium placing within a Fabry-Pcrot cavity, which is driven by a pump laser. We find that the system appears the optical bistability by mean-field approximations. In addition, we also discuss the quantum feature of the cavity field spectra in different initial state of the system, the coupling strength and the Kerr constant.Finally, the conclusions and discussion are given.