Nonlinear Multistability Of Cavity Optomechanical Systems

With the continuous development of fabrication technology, frequency ofmechanical oscillators in cavity optomechanical systems has grown from a fewHertz to GHz, and its quality has also become smaller from several kilos to1020g. In addition, due to the cavity optomechanical systems have importantapplication prospects in precision measurement and quantum information terms,people have conducted extensive research on various cavity optomechanicalsystem such as cooling the mechanical oscillator to the ground state, themechanical oscillator modulation on the light field, the Casimir forcemeasurement and so on. These systems have been exploited as a tool to observethe quantum phenomenon and regulate the quantum properties of macroscopicobjects, which can be used to verify the basic laws of quantum mechanics, todeepen understanding and applications of the basic laws of quantum mechanics,such as achieving the preparation of squeezed states, entanglement states andother non-classical states. In this thesis, we study nonlinear multistability ofhybrid optomechanical systems where a Y-type or Ladder type atomic ensemble isconfined in a cavity.First, we explore the Y-type four-level atomic auxiliary cavityoptomechanical system under the conditions of large atom-number limit andlow-excitation case. Through solving Heisenberg-Langevin equations insteady-state case and the susceptibility of the atomic ensemble, selecting theappropriate parameters, we conduct numerical simulations, and find thatsteady-state position of movable cavity wall and the susceptibility of atomicensemble bound in the cavity present multiple steady-state solutions. At the sametime, we also find the number of steady-state solutions of the whole cavity optomechanical system can be changed by adjusting the spring elastic coefficient.When the spring elastic coefficient is taken a large value, multistable phenomenawill disappear.Secondly, the multistable response of a Ladder-type atomic assistedoptomechanical system is studied. Through theoretical analysis and numericalsimulation, we find that the steady state behavior of the movable cavity wall andthe atomic ensemble is not only related to the spring elastic coefficient, but also isassociated with the Rabi frequency of the classical pump field. When the springelastic coefficient decreases or Rabi frequency increases, the cavityoptomechanical systems will show multistable phenomenon, and the number ofsteady-state solutions in different regions is different.Finally, we give a brief summary and prospect about this dissertation. Theresults of our research may be helpful to know some quantum nonlinear effects inhybrid systems, it will promote the development of the field of nonlinear optics ina certain extent, and broaden the optical multistable applications in quantuminformation processing, optical computing and precision measurement etc.