Engineering of synthetic magnetic flux in Bose-Einstein condensates [Lin et al., Nature (London) 462, 628 (2009)] has prospects for attaining the high vortex densities necessary to emulate the fractional quantum Hall effect. We analytically establish the hydrodynamical behavior of a condensate in a uniform synthetic magnetic field, including its density and velocity profile. Importantly, we find that the onset of vortex nucleation observed experimentally corresponds to a dynamical instability in the hydrodynamical solutions and reveal other routes to instability and anticipated vortex nucleation.

• Received 23 November 2010

DOI:https://doi.org/10.1103/PhysRevA.84.021604