Dynamics Of Bose-Einstein Condensates In Optical Lattice With Artificial Magnetic Field

Recently,since the artificial magnetic field was successfully generated in optical lattices,the relevant reseach of neutral atoms in optical lattices,which is used to simulate the motion of charged particles in electromagnetic field,is soon attracting growing attention.In such a system people can study the theoretical mechanism of high temperature superconductors,spin liquids and topological insulators.In this thesis,dynamics of Bose-Einstein condensates in optical lattices with artificial magnetic field is investigated.The main contents are as follows:1.Introduce the knowledge of Bose-Einstein condensates and how to realize artificial magnetic field in neutral cold atomic system.The self-trapping phenomenon is also introduced.2.The dynamics of Bose-Einstein condensates in a one-dimensional optical lattice is studied.The kinetic equations and dynamic phase diagrams of this system are obtained by variational method with the discrete lattice model of mean-field approximation and tight-binding approximation.Combining the results of numerical simulation with theoretical conclusions,how the non-linear interaction of the system affects the different modes of diffsion,soliton or breather and self-trapping in such a system is investigated.3.Investigate the dynamical properties of dilute Bose-Einstein condensates trapped in a two-leg ladder configuration in the presence of an artificial magnetic field.The kinetic equations and dynamic phase diagrams are demonstrated.The conditions of phase transition can be controlled by adjusting the strength of Raman coupling and the non-linear interaction in this system.We use the variational method and numerical calculation to show how the dynamics is affected by Raman coupling and the non-linear interaction.4.According to the concept of dimension synthesis,the system with spin-orbit coupling effect in the optical lattice is considered.The dynamics of the spin-orbit coupling system is studied and analyzed,and the effects of spin-orbit coupling and non-linear interaction on the dynamics are observed.It is found that the existence of spin-orbit coupling leads to the existence of interesting loop structures in the dispersion spectrum of the system,which results the nonlinear Landau-Zener tunneling and the population oscillation of different spin states.