Dynamical Characters Of Spin-orbit Coupled Bose-Einstein Condensates In Different External Potentials

With the realization of spin-orbit coupling in ultra-cold atoms,Bose-Einstein condensate has drawn the growing attention.As is known,Bose-Einstein condensate trapped in different external potential appears many different dynamical phenomena,such as solitons and collective dynamics in harmonic potential,quantum tunneling dynamics in a finite depth potential well and the Bloch dynamics or Landau-Zener tunneling in optical lattices.However,there are many new phenomena in these dynamics with the consideration of spin-orbit coupling.In this paper,we mainly employ two external potentials to trap the spin-orbit coupled Bose-Einstein condensates with two components,one of them is one-dimensional finite depth potential well,the other is the optical lattices.We first discuss the ground state and the phase transition of the two systems,further the escape dynamics in a finite depth potential well and the Bloch dynamics in optical lattices are investigated.It is found that,spin-orbit coupling plays a role in enhancing the stability and destroying the symmetry of the dynamics in these two systems.The paper is organized by following chapters:In the first chapter,the physical background of the Bose-Einstein condensate and the experimental realization of the spin-orbit coupling in ultra-cold atoms are introduced briefly.The corresponding reports of the condensates in a finite depth potential well and optical lattices are surveyed.The characteristics of two external trap potentials are highlighted.In the second chapter,the variational method and numerical solutions are used to investigate the ground state and escape dynamics of two-component spin-orbit coupled Bose-Einstein condensates in a finite depth potential well.Combining the stationary equations and the ground state chemical potential,the stability diagram are provided and proved by numerical solutions obtained by Gross-Pitaevskii equation of the system.New dynamical phenomenons are observed,including the solitons in bound state,quantum tunneling in quasi-bound state and diffusion in unstable state.These dynamics are effected by interactions,strength of spin-orbit coupling and parameter of the potential well.In addition,spatial anisotropic tunneling and diffusion dynamics of the two pseudo-spin components induced by spin-orbit coupling are explained by the effect-mass of the condensates.Further,the mechanism that,spin-orbit coupling (Raman coupling)can stabilize(destabilize)the system is proved and discussed.In the third chapter,we use the variational method to analyze the Bloch dynamics of two-component Bose-Einstein condensates with spin-orbit coupling.First,we obtain equations describing the ground state of the system without tilt.It is found that the ground state phase transitions between zero-momentum phase and plane-wave phase still occur in this system.Then we tilt the optical lattice in different ground states phases,the condensates appear different characteristics of Bloch oscillation in different phases.In addition,the Bloch oscillations under the zero-momentum phase are harmonic,however they are anharmonic under the plane-wave phase.Further,spin-orbit coupling increase the amplitudes of Bloch oscillations under the plane-wave phase,but it can not affect the amplitudes of Bloch oscillations under the zero-momentum phase.Finally,we obtain the condition of the long-live Bloch oscillations and provide the corresponding phase diagram.It can be concluded that,spin-orbit coupling has a positive effect on maintaining long-live Bloch oscillations.These theoretical predictions and results are verified by numerical simulation.The fourth chapter sums up our work and outlooks for this field.