Researches On Quantum Correlations Of Cavity Optomechanical System Based On Periodically External Field Modulation And Dissipation Mechanism

Cavity optomechanics is a field at the intersection of nanophysics and quantum optics which has rapidly developed over the past few years.The field deals with the interaction between light and micro-or nanomechanical motion.A typical setup of optomechanical system is consisted of a laser-driven optical cavity with a fixed end mirror and a vibrating end mirror.With the development of experiment technologies and applications of new con-cepts and new methods,optomechanical coupling has been realized in a variety of novel systems by now.Besides,the parameters and scale of the system also cover a large range.The researches on cavity optomechanical system is a forward-looking and challenging fron-tier field in the world,which not only helps to reveal the physical essence of the transiton from quantum physics to classical physics,but also has important application prospects in ultrasensitive measurements,information processing,and so on.In this thesis,we mainly study how to utilize the periodic modulation of external field and the dissipative mechanism to realize single-mode squeezing of mechanical oscillators,two-mode squeezing between subsystems,quantum synchronization,one-way quantum s-teering,etc.Simultaneously,relations among different quantum correlations have been explored.The main work includes:1.The dynamic evolution of the optomechanical system with“membrane-in-the-middle”configuration is discussed in detail under symmetrically or asymmetrically peri-odic modulation of external field.The effects of periodic modulation of external field on single-mode squeezing of mechanical oscillators and two-mode squeezing entanglemen-t between two cavity fields are investigated.Numerical simulation results show that the steady-state bosonic squeezing and entanglement are significantly enhanced by using pe-riodically modulated external laser to drive either or both ends of the cavity.Remarkably,the fact that as long as one periodically modulated external laser driving either end of the cavities is sufficient to enhance the squeezing and entanglement is convenient for actual experiment,whose cost is that required modulation period number for achieving system stability is more.In addition,we numerically confirm the analytical prediction for optimal modulation frequency and discuss the corresponding physical mechanism.2.We propose an effective approach for generating highly pure and strong cavity-mechanical entanglement（or optical-microwave entanglement）in a hybrid modulated three-mode optomechanical system.By applying a two-tone laser pulse to drive the cavity and modulating the coupling strength between two mechanical oscillators（or between a me-chanical oscillator and a transmission line resonator）,we obtain an effective Hamiltonian where an intermediate mechanical mode acting as an engineered reservoir cools the Bogoli-ubov modes of two target system modes via beam-splitter-like interactions.In this way,the two target modes are driven to two-mode squeezed states in the stationary limit.In particu-lar,we discuss the effects of cavity-driving detuning on the steady-state entanglement and the purity.It is found that the cavity-driving detuning plays a critical role in the goal of acquiring highly pure and strongly entangled steady states.3.We present a theoretical scheme to simultaneously represent and significantly en-hance the level of quantum synchronization and entanglement between two indirectly cou-pled mechanical membranes,which are coupled to a common optical field within a cavity.By applying two-tone driving lasers with weighted amplitudes and specific frequencies,both synchronization gauged by Mari’s criterion and entanglement estimated by logarith-mic negativity can be greatly enhanced.We then clarify the relationship between quantum synchronization and entanglement in detail.Numerical simulation results show that the in-fluence of the coupling asymmetry G₂/G₁on quantum complete synchronization behaves similarly to that on the purity while the influence of the coupling asymmetry G₂/G₁on quantum phase synchronization is more similar to that on quantum entanglement.Besides,we demonstrate that although quantum synchronization and quantum entanglement are not directly related,both of them are sensitive to the the squeezing parameter and the cool-ing effect.Furthermore,it is also showed that detuning the frequencies of two mechanical oscillators can actually help quantum synchronization and entanglement,which is some-what similar to the case of quantum synchronization blockade.However,the fundamental physical mechanisms of these two cases are different.4.We propose a scheme for generating steady-state mechanical entanglement and one-way quantum steering in a coupled optomechanical system.By applying four-tone driving lasers with specific frequencies,we obtain an effective Hamiltonian that couples the delo-calized Bogoliubov modes of the two mechanical oscillators to the cavity modes via beam-splitter-like interactions.When the mechanical decay rate is small,the Bogoliubov modes can be effectively cooled to near the ground state by the dissipative dynamics of the cavity modes,generating steady-state entanglement of the mechanical modes.The mechanical entanglement obtained in the stationary regime is sensitive to the values of the ratio of the effective optomechanical coupling strengths.The results of numerical simulation with the full linearized Hamiltonian show that changing the ratio of effective optical-mechanical coupling strength will bring two kinds of competitive effects,and at the same time it will cause magnification oscillation of the average value of the mechanical oscillator.Under the steady-state mechanism,large entanglement between oscillators can be achieved by balanc-ing the two competing effects caused by changing the effective optical-mechanical coupling strength ratio and avoiding the amplified oscillation of the average value of the mechanical oscillator.Besides,the approach can also be used for implementation of one-way quantum steering between two mechanical oscillators when specific ratio of the effective optome-chanical coupling strengths and specific oscillator dissipation ratio are met.