Generation Of Magnetic Monopole In Bose-Einstein Condensate

Based on the three-dimensional Gross-Pitaevskii(GP)equation,Bose-Einstein condensate's dynamic behavior is studied in a time-dependent periodic external magnetic field.The vorticity of the condensates and the magnetic field of the monopole are consistent when the external magnetic field is strong enough.Multiple monopoles can be generated by using multiple zeros of the periodic magnetic field The positive and negative monopole pairs are studied.There are positive and negative magnetic monopoles.Positive magnetic monopoles refer to the monopoles whose magnetic induction lines are all emitted from the center of the circle,and only Dirac string is opposite to the magnetic induction lines and point to the center of the circle.Negative magnetic monopoles refer to the monopoles whose magnetic induction lines point from the outside to the center of the circle,and only Dirac string is emitted from the center of the circle.Firstly,the interaction between positive and negative monopoles and the formation of isolated Dirac strings are studied by means of mean field approximation.The results show that under the action of a time-dependent periodic external magnetic field,the Bose-Einstein condensate with ferromagnetic spin-1 will undergo topological deformation.With the evolution of time,when t(28)50ms,the two zero points of the magnetic field enter into the condensate,we can observe that the spin up state forms two small bumps on the z-axis in the density population diagram,which are up and down respectively.Then,the two zero points of the magnetic field coincide gradually when t(28)60ms,the upward and downward bulges are elongated,and finally spin-up state is linear on the z-axis.This corresponds to the isolated Dirac string predicted by theoretical analysis.We calculate the superfluid vorticity of the condensate and give the characterization diagram of the magnetic monopole.The result we get is that the condensate forms positive and negative monopole pairs at the two zero points of the magnetic field,which correspond to the upward and downward bulges of the spin-up state on the z-axis,respectively.With the evolution of time,the two zero points of the magnetic field begin to coincide slowly,and the two Dirac strings in the positive and negative monopole pairs approach each other gradually.It took about 5ms,they are connected completely,and form an isolated Dirac string finally.Then we introduce double potential wells to generate a magnetic monopole in each potential well.By adjusting the frequency difference f₁-f₂ to adjust the radial spacing d of the potential well,we adjust the amplitude of the signal during the change of the potential well to generate almost equal depth of the potential well,so that the two potential wells are close to the middle,and study the interaction of the magnetic monopole pairs in the potential well.When t(28)30ms,the density population diagram of the spin-up state forms upward and downward bulges on the z-axis,respectively.With the evolution of time,the upward and downward bulges are elongated.