Theoretical Research Of Squeezed Mechanical Mode And Four-wave Mixing In The Cavity Optomechanical System With Membrane

In the last decade,benefited from the technology progress of micro/nano fabrication,many different types of optomechanical systems could be studied,which vastly promote the development of cavity optomechanics.The cavity optomechanics has shown its more and more significant value for both fundamental research and application.On one hand,as a macroscopic object,the mechanical resonator offer a platform to study the quantum physics on the larger scale,which is important for research of the classical-quantum boundary.On the other hand,be benefited to a broadband wavelength working area,the cavity optomechanical system can connect different physical systems.Moreover,the optomechanical system could be keep the good coherence,and can be used to deal with the classical and quantum information.Furthermore,the optomechanical system can also applied for quantum precision measurement and sense domain.This thesis mainly focus on the cavity optomechanical system of membrane-in-the-middle structure(MIMS)and carry out some work as follow:(1)We introduce the elementary structure and character for MIMS,and then we research the dispersion coupling between cavity mode and mechanical mode.In the case of first-order dispersion coupling,we detailedly discussed three types of interactional process and their corresponding to physical effects.(2)We analyze the interaction effect between radiation pressure of twotone detuned optical fields and the quadrature component of mechanical mode,and obtain the special condition for back-action evading measurement.Based on that analytical result,we present the novel scheme which combine the coherent feedback and parametric amplification process to generate the strong squeezing of mechanical resonator.According to theoretical calculation,we detailedly analyze the influence of squeezed state and its purity from the coherent feedback and parametric amplification process.(3)We also study the four-wave mixing process in MIMS.The first,we research the interaction process types of be splitter and two mode squeezing are generate the optomechanical induced transparency and induced amplification effects,respectively.We present the method which combine two interaction processes and generate optomechanical four-wave mixing effect.Also,we analyze the influence of four-wave mixing process from different system parameters.Based on that analytical result,we keep researching the multimode four-wave mixing process in an unresolved sideband regime via one cavity mode coupled multi-mechanical modes.