The Research On Classical-Quantum Correspondence In The Driven Two-Well System Of Cold Atoms

In recent years,with the development of cold atomic experiment technology,the research based on the quantum system of cold atoms has aroused great interest,among which the research on the classical-quantum correspondence has become one of the important hot topics,and many interesting physical phenomena and laws have been found in many cold atoms subsystems.In this thesis,we study the dynamics of a two-well cold atoms system driven by a time-dependent external field,and discuss the classical-quantum correspondence properties of the system.This thesis is divided into four chapters.The first chapter is the introduction,in which we briefly introduce the theoretical methods,such as the atom cooling and trapping,BoseHubbard model,semiclassical processing method and Floquet theory.At the same time,the classical-quantum correspondence problem is introduced.In chapter 2,we study the dynamics of multi-body cold atoms trapped in a driven twowell system.Based on the semi-classical method,the nonlinear model of the two-well system is obtained.By adjusting the external field parameters,the regular periodic motion and chaotic dynamics of the system are demonstrated.Corresponding to the external field parameters of classical-chaotic region,we calculated the quantum coherence and entanglement find that compared to the other parameters in which the system is not chaotic,coherence and entanglement degrees will reduce,by numerical experiments in the different parameter region,we found that the system parameters of chaotic regions associated with the corresponding low coherence and entanglement of quantum system,the entropy is enhanced in the chaos parameter region.At the same time,the distribution of Husimi function of the system is analyzed numerically.It is found that the distribution of Husimi function is periodic in the regular region,but dissipates with time in the chaotic region.Finally,the Bhattacharyya distance of the system is calculated,and it is found that the corresponding parameters in the chaotic region cause its value to be larger than that in the regular region,which indicates that the perturbation sensitivity of the quantum system in the classical chaotic parameter region is greater than that in the classical regular parameter region.In chapter 3,we study the non-hermitian driven two-well quantum system.Based on the semi-classical method,we analyze the chaotic parameter region and the regular parameter region of the system,and discuss the tunneling dynamics of the quantum system.Through analytical and numerical calculations,it is found that the tunneling dynamics of the system is enhanced by parameters in the chaotic parameter region,which causes the population difference of atoms to oscillate with time,while the population oscillation in the regular parameter region is very weak.At the same time,the effects of the introduction of the non-hermitian parameters on the tunneling dynamics of the system are analyzed.It is found that the introduction of the non-hermitian parameters results in the transformation of the atomic system from the weak localization to a strong tunneling state.In order to understand the tunneling dynamics system,we discussed the Floquet energy spectrum of the driven quantum systems,found that the introduction of non-hermitian time-dependent driven frequency have obvious effects on system energy spectrum,it is interesting to note that when the non-hermitian imaginary part time-dependent frequency is integer times larger to the hermitian time-dependent frequency,the imaginary part of the corresponding energy spectrum is zero,which result in that the system becomes stable.In the chapter 4,we summarize work of this thesis and look forward to the future interest of our work.In this thesis,we study the dynamics of cold atoms in a driven double-well,analyze the chaotic parameter region and regular parameter region of the system,and discuss the coherence and entanglement of the quantum system corresponding to different parameter region.At the same time,we study the classical-quantum correspondence of the system caused by the introduction of the non-hermitian parameters.The related work can be further extended to more complicated quantum systems,and the results of related quantum manipulation provide theoretical reference for the study of atomic devices and related studies.