Classical Dynamics And Quantum Properties Of Cavity Optomechanical Systems In The Extremely-large-amplitude Regime

Cavity optomechanics has attracted much attention and undergone rapid development in recent years. It concerns with the coupling between optical cavity modes and mechanical degrees of freedom. It has applications in many areas, such as detection of gravitational wave, mechanical memory and quantum information processing. Most theoretical works on cavity optomechanics focus on the situation that the amplitude of the mechanical oscillation is very small, in which the optomechanical coupling can be approximately considered as linear or quadratic by expanding the resonant frequencies of the cavity modes around the static equilibrium position of the mechanical resonator.With a high-power driving laser, the amplitude of the mechanical oscillation can be very large, even may be comparable with the wavelength of the driving laser,i.e., the system reaches the extremely-large-amplitude regime. In this regime, the optomechanical coupling should be considered according to the exactly function relation between the resonant frequencies of the cavity modes and the position of the mechanical resonator. In addition, during one cycle of the mechanical oscillation, multiple optical cavity modes are excited or one single optical cavity is excited multiple times depending on the structure of the optomechanical system, which makes the dynamics of the system more complex.This thesis is mainly focused on the classical dynamics and quantum properties of optomechanical systems in the extremely-large-amplitude regime. The research conducted in this thesis is as follows:1. We set up a fabricating and measurement experiment platform of the whispering gallery mode microcavities to study cavity optomechanics. At present, we can fabricate microsphere, microdisk and microtoroid with quality factors of 108, 106 and 107, respectively. We can implement optical measurement of the microcavity by coupling it with a fiber taper of diameter near 1 μm. We observed periodic oscillation of the transmission spectrum caused by the optomechanical coupling.2. We studied self-sustained oscillation and dynamical multistability in movablemirror cavity optomechanical systems in the extremely-large-amplitude regime. In the phase space of the mechanical resonator, the limit cycles of the self-sustained oscillation is in the shape of sawtooth-edged ellipses. The mechanical resonator can exhibit dynamical multistability, meaning that it can reach different self-sustained oscillations depending on the initial conditions. By analyzing the mechanical oscillation process and the accompanying variation of the optical cavity occupation, we developed an analytical energy-balanced condition to ensure the stability of self-sustained oscillation. The effect of the mechanical nonlinearities on the dynamics of the mechanical resonator was also investigated.3. We studied classical dynamics and quantum entanglement in membrane-in-themiddle cavity optomechanical systems in the extremely-large-amplitude regime. By numerically solving the classical equations of motion of the system, we showed that the membrane can present self-sustained oscillations with limit cycles in the shape of sawtooth-edged ellipses and exhibit dynamical multistability. Then, the dynamical process of the quantum fluctuations around the classical orbit was studied. We calculated the quantum entanglement between the optical cavity mode and the membrane during the mechanical oscillation by using the logarithmic negativity. We showed that there is some synchronism between the classical dynamical process and the evolution of the quantum entanglement.