Maxwell-Schr(?)dinger Coupling Time-domain Spectral Element Method Analysis

With the development of quantum theory,more and more quantum technologies are applied to electronics,commurication and other fields.The quantum electromagnetic coupling problem,so-called light-matter interaction,is the key to achieve the quantum state control.Therefore,research on quantum electromagnetic coupling problem is of great importance for electronic interactions understanding and design of practical quantum computer,plasma and other related applications.In this thesis,based on the numerical sinulation model,the spectral-element time-domain method(SETD)has been used to derivate the Schrodinger equation and the Maxwell equation of electromagnetic field.After establishing the solution model of quantum electromagnetic coupling,the vector and scalar basic function can be solved simultaneously.Started with the quantum collision characteristics,quantum tunneling effect has been analyzed to demonstrate the correctness of solution for Schrodinger equation.The characteristics of microscopic particle under the quantum mechanics system have also been discussed.Next,a solution method of Maxwell-Schrodinger coupling equation based on Lorenz gauge for quantum electromagnetic coupling system has been introduced.Using this solution system,we have designed the light control pulse by both the conventional method and improved method to achieve the conversion of the electronic quantum state and the spatial distribution of time related parameters.The complete quantum state control of "the ground state-the first excited state-the ground state" has also been proposed and a more perfect design of optical control pulse has been realized.Then,the solution system of Maxwell-Schrodinger coupling equation based on Length gauge quantum electromagnetic coupling has been introduced.The system is used to analyze the complete state control by the optical control pulse of the improved method.By comparing with the Lorenz gauge methods,the correctness and superiority have been verified.The proposed method is also extended to the three-dimensional level for analysis of the related quantum harmonic oscillator.Finally,this thesis makes a systematic summary of the research work,and introduces the shortcomings of the existing work,and makes arrangements for the follow-up work.