Study On Ground State And Dynamical Evolution Of Vortex Ring In Bose-Einstein Condensate

Bose-Einstein Condensate(BEC)is an emerging physical research object.Since BEC was successfully observed experimentally in 1995,its high controllability makes it an excellent platform for studying novel physics.Recent researches have been carried out on potential modulation,rotation effects,and artificial spin-orbit coupling(SOC)effects.In this thesis,we numerically calculate the ground state density distribution of the two-dimensional(2-D)BEC system and the giant vortex(GV)in the rotating system,as well as the dynamical evolution of the vortex ring(VR)through a ball-like obstacle in the three-dimensional(3-D)BEC system.The main contents are as follows:In chapter 1,we first give a brief review of the research background of the BEC system.Then we introduce the rotation effects and related research results of GV state,as well as the SOC effects.Furthermore,VR in 3-D system and its dynamical properties are introduced.Finally,we introduce the Gross-Pitaevskii(GP)equation which is commonly used in the study of BEC system,and then the Rung-Kutta method and the time splitting spectrum method are introduced in detail.In chapter 2,we study the ground-state properties of 2-D BEC with SOC loaded in the harmonic-plus-radial potential.In the immiscible regime,odd-petal-number states can be found.By increasing the effective atom interactions,the odd-petal-number states transform into a phase where petals in the outer annular potential trough are coexisting with inner longitudinal stripes,and finally become the 'serpentine' stripe structures.In a rotating system,there is a transition from the vortex lattice structure to GV state as the rotation frequency is increasing.The critical rotation frequency of this transition depends on the SOC strength.A larger critical rotation frequency value is required at a system with larger SOC strength or larger atom interactions.In addition,we found that this type of harmonic-plus-radial trapping with a strong radial part is a suitable choice to create GV state.The radius and the winding numbers of the GV states are discussed in detail.In chapter 3,the dynamical evolution of a VR passing through a coaxial obstacle ball in a 3-D BEC system is given.We fix the radius of VR to be R=40 and discuss the evolution results through obstacle ball with different radius R0.If R0 is much smaller than the R,the diameter of VR is a little expanded when it is close to the obstacle,but when VR passed away from the ball obstacle,its diameter would return to the original value and VR moves forward.If R0 is similar to R,the process is a little complicated when VR meets the obstacle.The ring-shape VR becomes gear-shaped and the four gears locate at the diagonal directions of the YZ-plane.Then the planar VR would become 3-D helical structures when it is passed away from the obstacle.When it evolves to be planar,the size of the VR will decrease as the obstacle's radius R0 increases.If R0 is much larger than R,VR would dissipate and disappear eventually.In chapter 4,we study the dynamical evolution of a VR passing through a coaxial modified ball obstacle in a 3-D BEC system.By comparing the results of a set of obstacle spheres with the modification period of four(P=4)but with different modification amplitudes,we explore the reason for symmetry-breaking of VR when it goes through a coaxial ball obstacle with R0?R(which has been discussed in chapter 3).In addition,we also calculated the evolution of VR when it passes through the obstacle ball with other modification periods(P=3,5,6),and the results show that helical VR with periodic modulations can be generated when the planar circular VR passed through a modified ball obstacle.In chapter 5,we give a brief summary of the research contents of this thesis.