Three-dimensional Spinor Bose-einstein Condensate Dark Solitons And Vortices Under Complex Potentials

The Bose-Einstein condensate,one of the most remarkable physics,provides a highly suitable laboratory for the study of the internal properties and collective be-haviors of atoms,such as interpreting the superfluidity of liquid helium and the mi-crocosmic mechanism of superconductor,and so on.With the development of optical techniques for trapping of ultracold atomic gases,the Bose-Einstein condensate can have internal degrees of freedom associated with the hyperfine spin,called the spinor Bose-Einstein condensate,which can exhibit a rich variety of ground states and topo-logical textures,such as the spin domain,spin texture,coreless vortices and bright-dark vector solitons,and so on.As a result,these will provide multiple choices for the storage and processing of the quantum information.It is worth noting that the exter-nal potential play a key role in researching the spinor Bose-Einstein condensate.The common potentials include parabolic potential,Gaussian potential and optical-lattice potential,and so on.This paper investigates the stabilities,dynamics and spin tex-tures of the spiror Bose-Einstein condensate dark solitons and vortices.In addition,we successfully manipulate the spinor Bose-Einstein condensate vortices and coreless vortices along a specific direction.The main work includes the following:1.We construct the stable spin-1 ferromagnetic three-dimensional spinor Bose-Einstein condensate dark solitons with the different topological structure factors con-fined a complex potential including a three-dimensional harmonic trap and a two-dimensional Gaussian trap,via employing the energy functional method and direct numerical simulation of the coupled Gross-Pitaevskii equations,and analyze their dy-namics.In addition,we obtain the stability region of the one of these in the important parameter space.Furthermore,we obtain the cricoid spin texture structures pointing to the circle of spin vanishing by calculate the spin density vector of the dark-solitons.In order to more clearly describe the spin texture distribution,we calculate the vari-ational intensity of spin density vector size along with the space.These enable us to better understand the magnetism of the spinor Bose-Einstein condensate and provide the theory for the relational experimental research.2.We investigate the three-dimensional spinor Bose-Einstein condensate vor-tices and coreless vortices in a spin-1 ferromagnetic Bose-Einstein condensate under a complex potential consisting of a two-dimensional harmonic trap along the transverse radial direction and an one-dimensional optical-lattice trap along the z axis direction.First,we obtain the optimal solution of the wave functions via the energy functional method.Then,we employ the Crank-Nicholson discretization scheme to numeri-cally simulate the coupled Gross-Pitaevskii equations in order to verify the stabilities of the vortices and the coreless vortices obtained by the energy functional method.Moreover,we find two spin texture including three-dimensional cricoid spin texture pointing to the circle of spin vanishing,and three-dimensional cricoid spin texture pointing to the island in inner and the circle of spin vanishes in outer by calculating the spin density vector of the vortices and coreless vortices.Meanwhile,we calculate the variational intensity of spin density vector size along with the space to more clearly describe the spin texture distribution.Finally,we successfully manipulate the spinor Bose-Einstein condensate vortices and coreless vortices along the z axis direction by steadily moving the optical-lattice trap.Furthermore,we find the merging and splitting of the spin domain during the manipulation.Namely,we may control the spin texture by manipulating the external potential and better analyze the microcosmic mechanism of the spinor Bose-Einstein condensate system,which will further promote the devel-opment of the quantum information processing.