We numerically simulate vortex nucleation in a Bose-Einstein Condensate (BEC) subject to an effective magnetic field. The effective magnetic field is generated from the interplay between light with a non-trivial phase structure and the BEC, and can b
e shaped and controlled by appropriate modifications to the phase and intensity of the light. We demonstrate that the nucleation of vortices is seeded by instabilities in surface excitations which are coupled to by an asymmetric trapping potential (similar to the case of condensates subject to mechanical rotation) and show that this picture also holds when the applied effective magnetic field is not homogeneous. The eventual configuration of vortices in the cloud depends on the geometry of the applied field.
We calculate the low energy elementary excitations of a Bose-Einstein Condensate in an effective magnetic field. The field is created by the interplay between light beams carrying orbital angular momentum and the trapped atoms. We examine the role of
the homogeneous magnetic field, familiar from studies of rotating condensates, and also investigate spectra for vector potentials with a more general radial dependence. We discuss the instabilities which arise and how these may be manifested.
