The Matter-wave Pressure In Quantum-classical Hybrid System And Cavity Optomechanical System Dynamics

The birth of quantum mechanics is an important symbol of the development of physics,with the development of quantum mechanics and quantum information science,quantum theory plays a key role in the process of promoting the development of human society.The corre-sponding theory of quantum mechanics and classical mechanics and the study of quantum-classical hybrid system further reveals the relationship between the quantum mechanics and classical mechanics.The concepts of cavity-QED,cavity optomechanical systems,quantum-classical hybrid systems have also been studied extensively,and significant breakthroughs have been made in the experiments.In this dissertation,we proposed the concept of material wave pressure and present a theory of dynamics of quantum-classical hybrid system,tools are helpful for us to understand the mathematical structure of quantum and classical mechanics.At the same time,the concept of“material wave pressure”has been put forward.In addi-tion,the Quenching evolution of quantum-classical hybrid systems and the master equation for photon mediated phonon-atom coupled system are discussed.This dissertation consists of five chapters and the main are given in chapter III-V.In chapter I,a brief introduction of the background and progress of this work is present-ed,mainly includes quantum mechanics and quantum information,quantum-classical hybrid system and cavity optomechanical system.Several kinds of cavitating mechanical system models are briefly introduced.In Chapter II,the basic concepts and knowledge of the study has been introduced,including the basic theory of cavity optical-force system,basic concepts and principles of quantum mechanics and the theory for correspondence between the quantum mechanics and classical mechanics.In chapter III,the matter-wave pressure is investigated through examining the dynamics of a quantum-classical hybrid system.After giving a general mathematical form,the dynamic equations satisfying the classical subsystems of a single atom system as a quantum subsystem and a Bose-Einstein condensate as a quantum sub-system are investigated,respectively.Then we raise the concept of”matter wave pressure" after we compare the kinetic equations with the classical dynamical equations.When we take an atom for the quantum subsystem,the classical subsystem experiences a force(B0/Q3)proportional to the distance Q between the two walls,meanwhile the energy of the atom has been changed because the classical subsystem provides a moving boundary for it,even if the atom remains in the same level in time evolution.When we take the BEC for the the quantum subsystem,there would exert an additional force proportional to Q-2 to the moving wall.This force comes from the atom-atom interaction in the BEC which can show the nonlinearity in BEC.In our knowledge,this is the first time theoretically realistic matter wave pressure.In addition,it is shown that the matter wave pressure can be measured in our model by measuring the nanoscale displacement Q.This means that it is also a challenging task to detect material wave pressure through experimental observables.In chapter IV,another extreme varying conditions,namely rapidly varying conditions are presented.The evolution of the system in this condition can be defined as Quenching evolution.This forms a supplement to the study of Chapter III.We consider a quantum par-ticle in a one-dimensional infinitely deep potential,one boundary of the potential is assumed to move rapidly,such that the particle inside does not evolve with time.The condition for such evolutions has been examined while the matter-wave pressure for the quantum system has also been calculated.By considering a spin-1/2 in a rotating magnetic field,we explore the condition for the anti-adiabatic evolution.Discussions and remarks on this condition are given.In chapter V,the cavity-optomechanics in the bad cavity with single-photon limit is investigated.It can be shown that a cavity with large decay rate can induce phonon-atom couplings,the coupling constant depends on the cavity driving strength,atom-cavity coupling constant and frequency difference as well as the position of the moving-end-mirror.We derive a master equation to describe the phonon-atom coupling,the conditions for this master equations to validate is deduced and discussed.A discussion beyond the bad-cavity and single-photon limit is also given for comparison.Finally,the conclusions and discussion are given.