Nonclassical Properties And Quantum Entanglement In The Optomechanical System

In this thesis,we mainly study the nonclassical properties and quantum entanglement of the mechanical oscillator in a cavity optomechanical system assisted by an optical parametric amplifier(OPA).In Chapter 1,we first briefly introduce the recent development of cavity optomechanics,then we outline the standard optomechanical system and the cavity optomechanical system involving the degenerate optical parametric amplifier,respectively.Since the quantum states of the mechanical oscillator discussed in the thesis are all in the Gaussian type,therefore we first review the properties of Gaussian States and the methods for the entanglement measurement of the two-mode Gaussian States in Chapter 2,and then we give a detailed introduction to the squeezed states and the corresponding nonclassical properties.Finally,the mechanisms of the generation of mechanical squeezing with optomechanical systems are summarized.In Chapter 3,we mainly discuss the effect of the OPAs on the stability and the mechanical entanglement of two cascaded cavity optomechanical systems.Two spatially separated mirrors can be entangled while the coupled optomechanical system is driven by a(modulated)laser beam.However,the stability of the system and the mechanical entanglement are very sensitive to the temperature of the mechanical thermal reservoir and the fluctuation of the modulation parameters.Here,by placing OPAs in the cavities,we find that the parameter space corresponding to the stability of the system are further expanded.Under the conditions of strong laser driving,the system can be in stable for blue laser detuning and the mechanical entanglement between the mirrors can be pronouncedly enhanced with well-selected parameteric gain.Furthermore,the application of OPAs is helpful to preserve the mechanical entanglement suffered from the dissipation at some finite temperature.Hence,our scheme provides an alternative way for improving and engineering the quantum entanglement of two distant mechanical oscillators in addition to quantum reservoir engineering and periodic modulation with chirped driving laser.Our scheme is great interest for quantum information processing and the studies of the fundamental problems of quantum mechanics.In Chapter 4,we propose a scheme to enhance the mechanical squeezing by using an optical parametric amplifier in the standard cavity optomechanical system.In the standard optical mechanical system,the mechanical squeezing can usually be achieved in ways,such as by using periodically modulated driven laser or alternatively by placing an OPA inside the cavity.Here,we find that the mechanical squeezing can be further enhanced by combining the above two approaches.On the one hand,compared with the case without periodic modulation,the periodic modulation can be used to realize the squeezing of the mechanical oscillator even if there is no feedback control.On the other hand,the coupling between the cavity field and the OPA will lead to the squeezing of the light field,which transfers to the phononic field by the optomechanical interaction leading to further squeezing of mechanical oscillator.Therefore,the squeezing strength of the mechanical oscillator is greatly increased by our method.Moreover,we also find that even in the case where the temperature of the mechanical oscillator is T = 0.1K,the mechanical squeezing can still reach 4.3dB,which can be used for ultra-high precision measurement where a squeezing of 3dB is prerequisite,and it is survival even for higher temperature T = 1.5K.Therefore,the cavity optomechanical system involving periodic driving and OPA will find potentially significant applications in quantum information processing and quantum sensing.