The Study Of Quantum Entanglement And Nonlinear Properties In Optomechanical Systems

Optomechanical systems can be used for manipulation and detection of mechanical mo-tion in quantum regime as a high sensitive detectors for small forces and displacements, in addition to their effective applications in quantum information processing. The subject of this thesis is mainly the generation of entangled states between macroscopic objects and to understand the interaction between the light and mechanical oscillators in optomechanical systems. This work is of importance for quantum metrology and information theory because of the possibility of quantum computing. We first summarize the fundamental tools of cav-ity optomechanics and show how we can use them to investigate some physical phenomena in quantum regime. Then we exploit the quantum dynamics of the cavity optomechanical system formed by a Fabry-Perot cavity to study quantum entanglement and other nonlinear properties from a theoretical point of view.The first work of this thesis examines a coupled two-cavity optomechanical system to show its potential usages by revealing the physical processes. We address state transfer and quantum entanglement by exploring the dynamics of the system. Using a well established model, we describe the interaction of the optomechanical system, where the mechanical os-cillators can switch states of each other. Under two conditions, we deduce the corresponding-ly effective Hamiltonian with beam splitter and nondegenerate parametric-down conversion type, respectively. Including the whole interactions, we show that the state transfer and the stationary entanglement between the two mechanical resonators can be achieved.In the second work we investigate the bistable properties and the entanglement in a two modes cavity optomechanical system. Our results show that the bistable regime in terms of pumping amplitude can be adjusted by tuning the frequency of the pumping fields. Although the two modes of the cavity interact with the same mechanical mode, with existence of a correlation between the two modes, no entanglement is observed between them, while each of the two cavity modes entangled with the mechanical mode separately.In the third work we discuss the generation of squeezing and continuous variable (CV) entanglement by numerically calculating the variance in the quadrature amplitudes of the field modes. We also evaluate single mode and two-mode squeezing which can be employed in quantum information science to enhance the quantum communication and leads to global quantum internet.Finally, we conclude with a discussion of the possible applications and future prospec-tives.