Elementary Excitations of a Bose-Einstein Condensate in an Effective Magnetic 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.