Nonlinear Bloch Dynamics And Spin-wave Excitation In A Bosonic Ladder With Magnetic Flux

The realization of artificial gauge field in optical lattice provides an ideal platform to explore the physical phenomena in condensed matter systems.Meanwhile,quasi onedimensional lattice systems,such as the bosonic two-leg ladder system in the artificial gauge field,have abundant quantum phase transitions,which arouse people’s great interest.The two-leg flux ladder is the simplest and most ideal model to reflect the coupling effect of lattice and magnetic field,which is of great significance to the study of some novel phases,topological and chiral characteristics in condensed matter physics.In particular,the degree of freedom of the left and right legs of the ladder can be regarded as pseudospin,so the two-leg flux ladder also provides an ideal platform for the study of spin mechanics.The study of the dynamics of flux ladder system provides more opportunities for exciting new dynamic phase transitions,accurately controlling and identifying the particle dynamics and ground state phase transitions.Nevertheless,there are still aspects that need to be studied.Given the interatomic interactions,the competitive relationship among interatomic interaction,magnetic field,and rung-to-leg coupling ratio for inducing the ground-state phase transition is not clear.In particular,the non-equilibrium dynamics of different ground states under external modulation is still a subject to be studied.Therefore,this paper focuses on the phase transition and dynamics phenomena in the bosonic ladder system.The main content of this paper is as follows:The first chapter introduces the relevant research background of this thesis.Firstly,the Bloch oscillations of Bose-Einstein condensates in optical lattices are reviewed.Then,the experimental realization of the bosonic flux ladder is emphasized,and the bosonic flux ladder with interatomic interaction is further introduced.Finally,the Bloch oscillations in the bosonic flux ladder are introduced.In order to better study the dynamics of flux ladder system,the Bloch dynamics in an one-dimensional deep optical lattice with complex interactions is first considered in the second chapter.The effects of two-body and three-body interactions on Bloch dynamics in one-dimensional deep optical lattices are studied systematically by means of the mean field theory and the tight-binding approximation,combined with the variational principle.The results show that the decoherence caused by two-body interaction plays a dominant role,while the decoherence caused by three-body interaction is relatively weak.Furthermore,it is found that the persistent Bloch oscillation can occur when both the twobody interaction and the three-body interaction exist and certain conditions are met.In addition,we also discuss the dynamic localization of Bloch packets under the action of periodic modulating linear forces.It is found that the system has rich Bloch dynamics,including strong Bloch oscillation with large amplitude,drag of Bloch wave packet and significant dispersion of wave packet.The results lay a foundation for further study of the dynamics of bosonic ladder and complex lattice chain system.In the third chapter,the ground state and dynamics of the interacting bosonic ladder system subjected to constant or periodically modulated linear forces in a synthetic magnetic field are investigated analytically and numerically.In the absence of external linear force,the ground state of the system is studied,and two states of the system,namely zero-momentum state and plane-wave state,are given,and the threshold of the conversion of the two states is obtained through analysis.The physical mechanism of ground state transition is clearly revealed.The Bloch oscillations and spin dynamics initialized in different ground states under linear external forces are discussed.The results show that the Bloch oscillation is chiral and dependent on the ground state.The dynamic localization of Bloch packet under the action of periodic modulating linear force is discussed in the bosonic flux ladder system.There are abundant Bloch dynamics and spin mechanics.Correspondingly,periodic but non-harmonic spin mechanics are observed.The fourth chapter is the summary and prospect.