Ground States Of Two-component Bose-Einstein Condensates In Harmonic-like And Toroidal Potential

Shining a Gaussian laser at the center of the harmonic trap and adjusting the intensity and width of it,two different geometry potential can be reached,i.e.harmonic-like potential and toroidal potential.Bose-Einstein condensates trapped by the two different external potentials will exhibit different ground states.In the BEC system,not only the external potential,but also the dipole-dipole interaction(DDI)and spin-orbit coupling(SOC)play an important role.In this paper,we focus on the system of BEC with DDI or SOC and analyse their ground states.The main contents includes the following aspects:First,the vortex structures of the dipole Bose-Einstein condensate trapped by harmonic-like potential and toroidal potential is studied,respectively.In the harmonic-like potential,the increasing DDI can induce the transition from azimuth separation to radial separation and then to mixing.Basing on the tunable DDI,vortex pair,vortex lattice,double quantum vortex as well as sandwich-like structure can be observed in the ground-state density profiles.It is worth noting that the double quantum vortex turn into two single quantum vortices with the increasing DDI.In the toroidal potential,single quantum vortices arrange themselves along the ring and a multiple quantum vortex is located at the center of potential.With the increase of DDI,the multiple quantum vortex gradually became a double quantum vortex,and the two components gradually become miscrible.Especially,despite the further increases of DDI,the double quantum vortices still remains,which is different from the case in the harmonic-like potential.Secondly,the ground states of Rashba and Dresselhaus spin-orbit coupled condensates trapped by the toroidal potential are investigated.It is found that,in the absence of magnetic field,the Rashba and Dresselhaus spin-orbit coupled condensates share the same ground states,such as the petalstructure with azimuth modulation.When the quadrupole magnetic field appears,the original symmetry of Rashba SOC is broken and a new discrete symmetry is established,while for the case of Dresselhaus SOC,the original rotational symmetry remains unchanged.This made the two system with different SOC exhibit different ground states.For Rashba SOC,the condensate exhibits a rectangular ground-state density profiles in the case of the weak contact interaction,and the half-quantum vortices appear and are pinned to the coordinate axis by the quadrupole magnetic field for the strong interaction.For the Dresselhaus SOC,the condensate has a ring structure under the weak interaction,and the half-quantum vortices are arranged along several concentric rings in the case of strong interaction.Therefore,we propose to use the quadrupole magnetic field to distinguish the two different SOC.Finally,taking the sextupole magnetic field as an example,we analyse the effect of the multipole magnetic field on the ground states of the Rashba spin-orbit coupled condensate.It was found that,the system has 2p/ 3discrete symmetry;the ground-state density profiles look like hexagon for the weak interaction,but for the strong interaction the half-quantum vortices appear and arrange themselves at the position of the radial magnetic field and the rotating direction is determined by the sextupole field.However,when the effective potential formed by the magnetic field cancels out the constraint from the toroidal potential,the condensates may collapse.For the2n-pole magnetic field,Rashba spin-orbit coupled condensate has 2p/ n discrete symmetry.The larger n is,the stronger the ability of the magnetic field to weaken the toroidal potential.In this case,it is necessary to select a suitable trapping potential.