Spin Vortex In ⁸⁷Rb Dipolar Spinor Bose-einstein Condensate

Spin vortex state,as a type of topological non-trivial spin structure,has extensive appli-cations in the fields of magnetic materials,spintronics,quantum computing,and others.In2006,in the quenching experiment of Bose-Einstein condensate,people discovered that this vortex state could exist as an unstable topological defect in the Bose-Einstein condensate.In the Bose-Einstein condensate,it was found that dipole-dipole interactions were favorable for the formation of spin vortex states.They discovered that the conditions for the generation of spin vortex states significantly beyond the range obtainable in experiments using numerical simulations.We manage the following studies to generate spin vortex states in a laboratory situation.First,We carefully investigate the challenges of forming spin vortex states.It is discov-ered that although the formation of spin vortex states in a harmonic potential trap is favored by magnetic dipole-dipole interaction,undertaking so would result in an increase in the local spin-spin interaction energy（E₂）.The rise in E₂is caused by the three components of wave function（spin-1）failing to coexist in a single density mode.Next,we design a potential trap that suppresses density at the trap’s core..It is accomplished by inserting a blue-detuned light plug with adjustable width and intensity into the harmonic potential trap.The local spin-spin interaction would not prevent the development of spin vortex states under specific plug opin-ions.The number of atoms needed to create spin vortex states was one order of magnitude less with this method than with earlier ones.Finally,to explain our numerical results,We carry out a qualitative,theoretical analysis of our plan’s effectiveness.We apply fast Fourier transform to accelerate the calculation of dipole-dipole interac-tions.This discrete Fourier transform however tends to generate more numerical errors.Since the harmonic potential trap we utilize is compressed in the z direction,it is unable to ignore the errors caused by the discrete Fourier transform.To improve numerical accuracy,we propose an analytical expression for dipole-dipole interactions truncated for this type of potential trap.The relative error is an order of magnitude smaller with the truncation method.We investigate the effect of microgravity on the formation of spin vortex states and dis-cover that it causes a quantum phase transition.During the phase transition,the spin vortex state takes on an off-axis form.The similarities and differences between the off-axis spin vor-tex state and the conventional spin vortex state have been thoroughly investigated.We find that the off-axis spin vortex state has the same topological structure as the spin vortex state,but the vortex core of the off-axis spin vortex state is not located at the center of the harmonic trap,but rather at the center of the added optical plug,which can be moved.The divergence of spin density at every point in space is zero in the spin vortex state,but not in the off-axis spin vortex state.Finally,in order to explain the shifts in physical quantities during the phase tran-sition,we undertake a theoretical analysis of the mechanism of microgravity-induced phase transition.