Quantum Dissipative Dynamics Of Two Coupled Single-mode Optical Cavities

The system of two coupled single-mode optical cavities in a general environment,which is a class of systems in quantum dissipation theory,can be solved analytically,and the equations of motion of the dissipative cavities have been usually derived by the common methods such as Feynman-Vernon influence functional.In this paper,a new approach is proposed to solve multi-body linear systems to obtain exact quantum dynamics.Firstly,the coupled single-mode optical cavities interacting with the surrounding environment are transformed into a dissipative single-mode optical cavity describing the center-of-mass motion of the total system and an isolated single-mode optical cavity characterizing the relative motion within the system by introducing a new set of transformation relations for the creation and annihilation operators.However,unitary transformation makes the system-bath total Hamiltonian decouple the internal coupling mathematically,there are still in essence inductive couplings in the optical cavity systems.Based on the stochastic decoupling,the interaction between the coupled optical cavities and the environment is removed by virtue of random variables,and the equations of motion for the system and the environment in the common random field are obtained.The equation of motion of the reduced density matrix for the system is found using the statistical averaging,based on the line from one to more and the exact master equation of single-mode optical cavity interacted with a heat bath derived by stochastic description,the exact quantum master equation of the coupled optical system is attained through the variable inverse transformation.Finally,the evolution dynamics depends on the characteristics of the system and the environmental features described by the spectral density function.The main contents of this thesis are as follows.1.Some theoretical knowledge of quantum dissipative systems are introduced,i.e.,quantum dissipative systems,non-Markovian quantum state diffusion method,Feynman-Vernon influence functional,stochastic decoupling,non-Markovian and Markovian quantum dynamics.The discussion focuses on the key concepts and dynamical methods involved in this paper,which are the basis of the research work in this paper.2.The exact quantum master equation for the dissipation model of two coupled single-mode optical cavities in a heat bath is derived in the framework of the stochastic description.In this paper,a novel approach is used to show the detailed derivation of the exact quantum master equation.Further,the model is extended to N coupled single-mode optical cavity model surrounding a dissipative reservoir.Finally,the effects of spectral width and detuning on non-Markovian dynamics are discussed in the two coupled optical cavity systems interacted with the harmonic oscillators environment in Lorentzian-form spectral density.The results are shown as following.(1)When the detuning is fixed,the spectral width is decreased,but the amplitude of the decay rate of quantum dissipative dynamics is increased.Moreover,the period is faster,and the non-Markovian memory effect is exhibited more obvious.(2)As the increasement of the spectral width,the amplitude of quantum dissipative dynamics is reduced and the period is slower.Meanwhile,the memory effect time becomes shorter,and the steady state is finally maintained.(3)When the spectral width is fixed,the size of the detuning does not change the quantum dissipative dynamics.Therefore,the non-Markovian memory effect always exists.Only if the detuning is increased,the oscillation of the decay rate for quantum dissipative dynamics is intensive,and the information exchange with the outside environment is more rapid.3.The exact quantum master equation of the two driven coupled single-mode optical cavity dissipation models is derived in the framework of the stochastic decoupling.Next,the model is generalized to give the exact quantum master equation for the dissipation model of N coupled single-mode optical cavity driven by a time-dependent external field.Finally,the quantum dissipation dynamics rates of spectral width and detuning in the spectral density function on the effect of time-dependent external field are simulated numerically.The results are presented as following.(1)When the driven field and detuning are fixed,the spectral width is increased.Moreover,the amplitude is reduced,and the oscillation occurs in a short time,when the time increases,the amplitude magnitude and the period remain constant,acting uniformly with the outside world.(2)When the driven field and the spectral width are fixed,the detuning and the amplitude are increased,and the dissipation rate is periodically variable.