Isolated Dirac string induced by interaction between positive and negative monopoles

Abstract

<sec>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 <i>z</i>-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 <i>z</i>-axis, which is consistent with the scenario of the isolated Dirac string predicted by theoretical analysis. </sec><sec>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. </sec><sec>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 <i>z</i>-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.</sec>