Synthetic magnetohydrodynamics in Bose-Einstein condensates and routes to vortex nucleation

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.