Controlled vortex states in Bose-Einstein condensates

There is no known experimental technique to create and control shape and orientation of the vortex lattice in Bose-Einstein condensates and the subject of this paper is the numerical study of creation of controlled vortex states with time varying potentials of various geometries formed by laser beams. Gross-Pitaevskii equation in ultra-cold limit models well the behavior of Bose-Einstein condensates and is solved with time-splitting Hermite pseudo-spectral method where we model the creation of vortex states by exciting collective modes. Random behavior of laser beams is introduced to find under what conditions the rotating solutions remain stable.