由正负磁单极对相互作用诱导的孤立狄拉克弦

基于三维旋量Gross-Pitaevskii(GP)方程研究在含时周期性外磁场作用下玻色-爱因斯坦凝聚体的动力学行为.结果显示,在含时周期外磁场的作用下,铁磁态自旋为1的玻色-爱因斯坦凝聚体将发生拓扑形变.当磁场的两个零点进入凝聚体后,自旋向上态的密度布居图在z轴上分别形成向上和向下的凸起.随着磁场的两个零点在凝聚体内逐渐重合,向上和向下的凸起被拉长,最终自旋向上态在z轴上呈线状分布,这与理论分析预测得到的孤立狄拉克弦相对应.最后,通过计算凝聚体的超流涡度给出磁单极的表征图.结果显示,凝聚体在磁场的两个零点处形成正、负磁单极对,分别对应着自旋向上态在z轴上向上和向下的凸起.随着磁场的两个零点重合,正、负磁单极对中的两条狄拉克弦逐渐靠近,之后大约经5 ms,它们完全相连,最终形成孤立的狄拉克弦.

Isolated Dirac string induced by interaction between positive and negative monopoles

Based on the three-dimensional spinor Gross-Pitaevskii(GP)equation,the dynamic behavior of the Bose-Einstein condensate under the action of a time-dependent periodic external magnetic field is studied.The results show that the Bose-Einstein condensate with spin-1 in a ferromagnetic state will undergo topological deformation under the action of an external magnetic field periodically varying with time.When the two zero points of the magnetic field enter into the condensate,the density pattern of the spin-up state forms small convexities protruding upward and downward on the z-axis,respectively.As the two zero points of the magnetic field gradually coincide in the condensate,the upward and downward protruding convexities are elongated.Finally,the spin-up state in the shape of a line is distributed on the z-axis,which is consistent with the scenario of the isolated Dirac string predicted by theoretical analysis.As far as we know,magnetic monopole can be divided into positive monopole and negative monopole.The positive magnetic monopole means that all magnetic induction lines are emitted from the center of the circle.And only the Dirac string points to the center of the circle.The negative monopole is that all the magnetic induction lines point from the outside to the center of the circle,and only the Dirac string emits from the center of the circle.Magnetic monopole is a topological defect in vector field,which accords with both quantum mechanics and gauge invariance of electromagnetic field.Single magnetic monopole has been studied a lot in theory,and its analogues have been observed in experiment.But multiple monopoles and the interaction between them are still rarely studied.In this paper,multiple monopoles are produced based on the fact that the periodic magnetic field has multiple zeros.We use a new periodic magnetic field to generate a positive and negative magnetic monopole.Due to the strong external magnetic field,the vorticity in the condensate is consistent with the magnetic field of the monopole.Finally,by calculating the superfluid vorticity of the condensate,the characteristic diagram of the magnetic monopole is obtained.The results show that the condensate forms a pair of positive and negative magnetic monopoles at the two zero points of the magnetic field,corresponding to the two small convexities protruding upward and downward on the z-axis of the spin-up state,respectively.As the two zero points of the magnetic field coincide,the two Dirac strings in the positive and negative magnetic monopole gradually approach to each other,and after about 5 ms,they are completely connected,finally forming an isolated Dirac string.This result provides a new idea for further studying the isolated Dirac strings.