Dynamic Modulation Of A Time-dependent Two-level System

The study of population transfer in the quantum system is one of the frontier subjects of quantum control.It has important significance for the development of quantum optics,atomic physics and other fields.The Landau-Zener transition model is the classical model to implement population transfer.Since the Landau-Zener model was established,the study of tunneling based on different quantum systems such as Bose Einstein condensation,superconducting quantum circuits,spin system,etc.has been active.This model has basic significance for the study of time-dependent quantum system control.It describes the quantum transition between adjacent time-dependent energy levels driven by mean field.Its energy levels change linearly,and the coupling between energy levels is a constant.There are many research results about the tunneling characteristics of Landau-Zener model.And there is an analytical solution namely Landau-Zener tunneling formula for the population transfer of this model.When the field modulation is added,there can be oscillations in the evolution of the energy levels and the coupling between energy levels.The tunneling characteristics of these systems will be more abundant.This paper mainly introduces and discusses the population transfer situation in different system models and different system parameters so that we can get the optimal quantum tunneling mechanisms of these quantum systems and achieve efficient control of quantum systems.The main contents are as follows:Chapter one is the introduction part.Firstly,the article mainly introduces the research status quo of the problem about population transfer control based on different forms of two-level systems.Besides,the two-level quantum systems including the typical models of time-independent two-level systems and time-dependent two-level systems are introduced.In chapter two,the paper mainly discusses the quantum adiabatic theorem and the typical Landau-Zener tunneling model.And the analytical solutions of Landau-Zener tunneling can be derived.Then,the dynamical process of Landau-Zener model is analyzed by the method of numerical simulation and the Landau-Zener transition density pictures under different parameters are shown.The numerical and theoretical results can match well.In chapter three,the paper mainly introduces the quantum tunneling model under the condition that its energy levels change periodically and the coupling between energy levels is a constant.The white noise model and perturbation theory are used to get the rate of Landau-Zener transition.Then,the time evolution of the population can be described by using the rate equation approach.At last,the tunneling results under different parameters varying are explained by the method of analyzing its adiabatic energy levels and its dynamical processes.In chapter four,this article firstly introduces the two-level system model for the case that its energy levels are driven by a mean field and the coupling between energy levels evolve periodically.Martijn Wubs et al.have obtained the analytical results of the tunneling rate of this model.However,they did not discuss the situation that a constant term is added to the coupling term.Farrokh Sarreshtedari got the different tunneling results from that of Wubs' when there is a constant shift in the coupling term.The work in the last section of this chapter is a simple innovation.The situation that the constant coupling is equal to the amplitude of oscillating coupling term is considered.There are similar tunneling characteristics between this special model and Wubs' model.The tunneling phenomenon is mainly explained by its energy level evolution and dynamical processes.The chapter five simply introduces the adiabatic passage technology.And the composite adiabatic passage technology is applied to the special model discussed in the last part of chapter four.And the population transfer of that system is bigger when we apply the adiabatic passage technology.Finally,we summarize the article contents.And we give a prospect about the unfinished problem in this paper.