Vortex dynamics on a shell-trapped Bose-Einstein condensate with dipole-dipole interactions and thermal melting of a two-dimensional vortex lattice - Bereta, Sálvio Jacob (2024)
There are many efforts to understand better the dipolar long-range interaction, the shell potential confinement, and the vortices in Bose-Einstein condensates (BECs). Furthermore, combining these three areas suggests that it can give rise to new phenomena. In this thesis, we studied the dynamics of vortices in a shell-trapped dipolar BEC. The long-range dipolar interaction induces an inhomogeneous density distribution on the shell, affecting the vortex velocity field. We analyzed the dynamics of one and two pairs of vortices symmetrically located in the shell to separate the vortex-vortex interaction contribution from that of the density gradient due to the inhomogeneous background. In addition to the numerical studies, a Lagrangian formalism allowed us to derive semi-analytical expressions which are in agreement with the results of the Gross-Pitaevskii equation (GPE) simulations, giving us better insights into the influence of the core in the vortex dynamics outside the validity of the point-vortex model. In the second part of this thesis, we describe an actual experimental implementation of the shell BEC. Using the Stochastic Projected GPE simulations, we determine the configuration of a finite temperature vortex lattice produced in this potential over the action of gravity. More specifically, we studied the transition from a perfectly hexagonal (triangular) lattice to the hexatic and liquid phases by detecting the vortex positions to calculate the angular and pair correlation functions of this system for different values of temperatures and trap rotation frequencies. Our results for the vortex lattice melting are consistent with the hexatic to liquid transition in the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario and can be extended to predict the melting temperature of other finite-size systems.