The Dynamics Of Vortex Dipoles In Bose-Einstein Condensates

Vortex dipole is comprised of vortices with opposite circulation.Vortex dipoles are commonly observed in a wide range of contexts including,but not limited to,ocean currents,soap films,optical fields,and atomic Bose-Einstein condensations,and have been described as the primary vortex structures in two-dimensional chaotic flows.Given the prevalence of vortices and antivortices in BKT transition,phase transition dynamics,and superfluid turbulence,a quantitative study of vortex dipoles will contribute to a broader and deeper understanding of superfluid phenomena.In this thesis,we study the interactions of vortex dipoles,and the formation of vortex(or vortex dipole)in the interference process of dipolar Bose-Einstein condensates by numerically solving the Gross-Pitaevskii equation.Firstly,we investigate the collision of two vortex dipoles propagating in opposite directions along parallel lines.By means of varying the impact parameter,we identify three general dynamical modes of the vortex dipoles in a homogeneous BEC,which are the vortex recombination mode,the encircling mode and the flyby mode.The existence of these three modes has been corroborated by numerical computations of the ordinary differential equations describing the vortex interactions.Furthermore,we show the corresponding parameter ranges for these modes.Second,we investigate the oblique collision and catching-up dynamics of two vortex dipoles in a uniform Bose-Einstein condensate.We find that the collision dynamics are deeply related to the moving directions and the sizes of the initial vortex dipoles.For the oblique collisions of two vortex dipoles with the same size,we observe recombination and annihilation of the vortex dipoles.For the catching-up processes of two vortex dipoles with different sizes,we observe vortex temporary annihilation and resurrection,as well as vortex permanent annihilation.The corresponding parameter-space phase diagrams of the dynamics are given by numerical simulations.On the other hand,we also study the oblique collision dynamics of two vortex dipoles in a non-uniform Bose-Einstein condensate confined within harmonic potential.The results show that the initial radial positions and collision angles have a significant impact on the collision dynamics.At last,we investigate the interference of the dipolar Bose-Einstein condensates released from a double-well potential and studied the effects of dipolar interaction on the interference phenomena.We find that the dipolar interaction plays an important role in the interference process.When the polarization direction of the dipolar atoms is in the normal direction of the condensate plane,with the increasing of the strength of dipolar interaction,the visibility of fringes reduces and the width of fringes becomes larger.When the strength of dipolar interaction is fixed and the effective polarization direction of the dipolar atoms deviates from the normal direction of the condensate plane,the interference phenomena become complicated due to the anisotropic dipolar interaction.Especially,for the situation of polarization direction parallel to the condensate plane and fixed,by means of changing the initial relative position of the two dipolar BECs,the interference fringes in the central regions become wave-shaped and vortex dipoles can be formed,or visible positive(negative)vortices form in the central region of the condensate.The research in this paper is helpful to understand the dynamics of quantum turbulence,and the effect of dipolar interaction on the vortex or vortex dipole formation in the interference process of dipolar Bose-Einstein condensates.It is expected that these studies could contribute to a further understanding of the non-equilibrium physics in quantum fluids.