Ground State And Collective Excitation Properties Of Spin-1 Spin-orbit Coupled Bose-Einstein Condensates In Harmonic Potential

In recent years,the experimental realization of artificial spin-orbit coupled Bose-Einstein condensate(BEC)not only provides a pure and highly controllable research platform for quantum simulations,but also brings many novel quantum effects.At present,the ground state characteristics and dynamics of the spin-orbit coupled BEC system have been widely studied.Especially,after the realization of the spin-orbit coupled spin-1 BEC,many physical phenomena that are not found in the traditional BEC have been discovered,such as the quantum Hall effect,elementary excitations and striped phases.It is found that the spin-dependent interaction leads to a rich ground-state phases and rotons structures.This provides a new way to further regulate the ground state of the condensate and its dynamics.However,in realistic experiments,BEC is trapped in a harmonic potential and the spin-dependent interactions can be experimentally tuned.Therefore,this paper considers the spin-orbit coupled spin-1 BEC system under the harmonic potential.First,we study the ground state phase of the system and analytically obtain the phase transition condition of the system.Then the collective dynamics of the system is further studied,revealing that the dynamic behavior of the system is closely related to its ground state phase,which provides theoretical evidence for the experimental manipulation of the dynamic behavior of the condensate.In the first chapter,we introduce the relevant research background,includeing experimental realization of artificial spin-orbit coupling in BEC,ground state phases of conventional condensates in free space,and novel ground-state quantum phases of systems under the synergistic effect of spin-orbit coupling and spin-dependent interactions.Finally,experimental observations of collective dynamics and a Halleffect-like dynamical response in spin-orbit coupled systems are presented.In the second chapter,we study the ground state phases of quasi-one-dimensional spin-orbit coupled spin-1 Bose-Einstein condensate trapped in harmonic potential.Based on variational analysis,the conditions of phase transition between magnetized and unmagnetized phases are obtained analytically,and the physical mechanism of inducing phase transition is revealed.The competition relationship among spin-independent interaction,spin-dependent interaction,spin-orbit coupling and harmonic potential for generating phase transition is discussed systematically.We predict that the spin-dependent interaction plays key role in ground state phase transition.Interestingly,the phase transition of the ground state degenerate to the single particle case in free space when spin-dependent interaction is absent.In addition,the harmonic potential strengthens the influence of atomic interactions on the phase boundary.In the third chapter,we study the nonlinear collective dynamics of quasi-onedimensional spin-orbit coupled spin-1 Bose-Einstein condensate trapped in harmonic potential analytically and numerically.The ground state of the system is determined by minimizing the Lagrange density,and the coupled equations of motions for the center-of-mass coordinate of the condensate and its width are derived.Then,two low energy excitation modes in breathing dynamics and dipole dynamics are obtained analytically,and the mechanism of exciting the anharmonic collective dynamics is revealed explicitly.The coupling among SO coupling,Raman coupling and spin-dependent interaction results in multiple external collective modes,which leads to the anharmonic collective dynamics.The cooperative effect of spin momentum locking and spin-dependent interaction results in coupling of dipolar and breathing dynamics,which strongly depends on spin-dependent interaction and behaves distinct characters in different phases.Interestingly,in absence of spin-dependent interaction,the breathing dynamics is decoupled from spin dynamics and the breathing dynamics is harmonic.The fourth chapter summarizes the main work of this paper,and prospects the next research work based on the current work.