Two-Photon Scattering In The Mixed Cavity Optomechanical System

The cavity optomechanical system,as a typical nonlinear quantum optical system,is a hybrid quantum system formed by photons and phonons coupled through radiation pressure.Optomechanical interaction is at the heart of the study of cavity optomechanics.The first-order and quadratic optomechanical couplings,whose coupling forms are proportional to the mechanical displacement and the square of the mechanical displacement of the resonator,respectively.So far,people have carried out systematic research on the first-order and quadratic optomechanical systems,and explored the extensive applications of optomechanical systems in quantum manipulation and quantum measurement.On one hand,in the first-order optomechanical systems,it has been found that the vibration of the moving mirror will induce a Kerr-type nonlinear interaction in the cavity,which could cause the photon blockade effect in the single-photon strong-coupling regime.In addition,the ultrastrong first-order optomechanical interaction can be used to generate the macroscopic Schr(?)dinger cat states in the mechanical resonator.On the other hand,in the quadratic optomechanical systems,it has been discovered that the photon blockade phenomenon also exists in this system,and the spectral features of single-photon scattering in the optomechanical cavity has been studied.In addition to the first-order and quadratic optomechanical systems mentioned above,there is a more general form of optomechanical coupling,namely the mixed optomechanical coupling.In the mixed optomechanical systems,both the first-order and quadratic optomechanical couplings exist.Recently,it has been discovered that there are some interesting physical effects in the mixed optomechanical coupling systems.For example,the sub-peak phenomenon has been found in the single-photon scattering spectrum in the mixed optomechanical cavity.In the scattering spectrum,it has also been found that the quadratic coupling term changes the height and location of the resonance peaks.In this model,the first-order and quadratic optomechanical couplings provide the physical mechanism for condition displacement and condition squeezing of the mechanical resonator,respectively.These interactions will produce interesting physical effects in the system,such as squeezing and cooling of the mechanical resonator,quantum nondestructive measurement,and optomechanically induced transparency,etc.The correlated photon source at the few-photon level is an important resource in the research of quantum information processing.How to generate the two-photon correlation is an important research topic in the field of quantum optics.Based on the energy spectrum of the mixed optomechanical system,in this thesis we propose to study the two-photon scattering problem in the mixed optomechanical system.We also explore the generation of correlated photon pairs in the mixed optomechanical system.The remaining chapters of this thesis are organized as follows:In the first chapter,we explain the research significance and background,the main content,and the chapter arrangement of this thesis in detail.In the second chapter,we first introduce some basic knowledges of cavity optomechanics,and then explain the mixed cavity optomechanical system which is the main topic of this thesis.We also introduce the single-photon scattering theory in the first-order optomechanical system,which is the basic knowledge for the two-photon scattering problem in the mixed cavity optomechanical system.In the third chapter,we introduce the mixed cavity optomechanical model and present the Hamiltonian of the system.We also study the twophoton dynamics of the system,derive the probability amplitude equations,and obtain the two-photon scattering solution.In addition,we also calculate the scattering spectrum of two photons.In the fourth chapter,we summarize the main content of this thesis and present the research prospects of this field.