Topological Phase And Transition For Atom In An One-dimensional Amplitude Modulated Optical Lattice

Topological phase transition as a phenomena occurs in quantum systems differs from the conventional thermal phase transition in that the topological phase transition is caused by the accumulation of a geometric phase during the adiabatic evolution of a quantum state along a closed loop in the parameter space of the system.When two two matters with different topological phases contact each other gaplessly,an edge state occurs around the material boundary of the non-trivial topological phase.The topological phase of the material depends on the Berry curvature integral in Brillouin space,so it indicates the global properties of the material.Just because of this characteristic,the topology of the material has strong robustness.In the recent progress,the research of using optical lattice to build modulatable system has been widely concerned,its advantage is that the adjustable parameters in optical lattice system make the system have higher flexibility We find that a generalized Su-Schrieffer-Heeger(SSH)model can be established in one-dimensional optical lattices,and topological phase transition point can be achieved by adjusting the magnitude of oscillation.We investigate the topological phase of noninteracting bosons in a one-dimensional periodically amplitude-modulated optical lattice.It is found that with the two band approximation and under near resonant condition,the system can be described by an extended Su-Schrieffer-Heeger(SSH)model.Like the conventional SSH model,the extended SSH model shows a non-trivial topological transition by adjusting the modulation amplitude and frequency suitably.The relevant parameters in current experiments are estimated and discussed.It is reasonable to believe that the topological transition could be observed under current experimental conditions.This paper is divided into four chaptersChapter one: We investigated the background,and discussed the motivation and the conclusion of our work.Chapter two: We briefly introduce some theoretical basis applied in this paper.Chapter three: We introduced our main research work about how to construct the generalized SSH model,which approximations are applied,and the relevant experimental parameter adjustment areas.Chapter four: The research content of this paper is summarized,the application prospect and follow-up work of our work are clarified,as well as the outlook of this research area.