Normal-mode Splitting Based On Optical Parametric Amplifier And Coherent Feedback In Optomechanical Systems

Cavity optomechanics is a combination of optical cavity and mechanics.It mainly studies the interaction between optical field and mechanical oscillators through radiation pressure,which is important research hotspots of quantum optics.Cavity optomechanical systems can be used to study macroscopic quantum behavior(such as optomechanical squeezing and entanglement,etc.)and can also directly generate optical squeezing and optical entanglement.In general,the system needs to enter the strongly coupled region to show many quantum phenomena,otherwise the quantum phenomena may be drowned out by classical noise.Therefore,strong coupling is the basic condition for cavity optomechanical system to generate and observe many macroscopic quantum phenomena(such as optomechanical squeezing and entanglement,etc.).Normal-mode splitting is an obvious signature that the systems has entered strong coupling.This thesis focused on the research of cavity optomechanical systems composed of optical cavity and a movable mirror,and carried out the following works:1.The normal-mode splitting of the displacement spectrum of the movable mirror and the intensity spectrum of the output light field based on the scheme of an optical parametric amplifier and coherent feedback is analyzed theoretically.After the Hamiltonian of the system is written out in the laser rotation frame,the Langevin equation of motion is obtained by using Heisenberg’s equation of motion and the corresponding feedback term,damping term and noise term,etc.,and solved in the frequency domain,the expressions of the position of the movable mirror and the output field are obtained.At the same time,the mode position and linewidth changes with parametric gain,parametric phase and input laser power are plotted under the condition of satisfying the stability of the system.It is found that the parametric gain,parametric phase and input optical power show a very similar variation trend with the feedback intensity.This similarity is due to the variation of the power of the cavity caused by different parameters.Both the range of normal-mode splitting and the corresponding mode splitting depend on multiple parameters,such as input laser power,feedback strength,parameter gain,etc.,and more obvious normal-mode splitting can be achieved through multi-parameter adjustment and optimization,which provides a theoretical basis for the realization of strongly coupled system in experiments.2.The impact of coherent feedback phase on the displacement spectrum and output field power spectrum of the movable mirror is further analyzed theoretically.The results show that for a fixed parametric amplifier gain,input light power and coherent feedback reflection coefficient,the normal-mode splitting interval and linewidth vary with the feedback phase.Generally,the mode splitting is more obvious when the coherent feedback phase is near zero.Compared with adding only positive feedback or negative feedback,the normal-mode splitting can be enhanced by optimizing the phase of feedback.It is convenient for us to increase optomechanical coupling strength and normal-mode splitting.These results provide a way to achieve stronger optomechanical coupling,which can be applied to ground state cooling of macroscopic mechanical oscillators,optomechanical quantum states and sensitive detection of weak forces.