Synthetic magneto-hydrodynamics in Bose-Einstein condensates and routes to vortex nucleation

TL;DR

This paper analytically studies the hydrodynamics of Bose-Einstein condensates under synthetic magnetic fields, identifying the conditions and routes leading to vortex nucleation, which is crucial for emulating quantum Hall effects.

Contribution

It provides an analytical framework linking hydrodynamical instabilities to vortex nucleation in condensates with synthetic magnetic flux, advancing understanding of vortex formation mechanisms.

Findings

Vortex nucleation corresponds to a hydrodynamical instability.

Identifies multiple routes to vortex nucleation.

Provides density and velocity profiles under synthetic magnetic fields.

Abstract

Engineering of synthetic magnetic flux in Bose-Einstein condensates [Lin et al., Nature {\bf 462}, 628 (2009)] has prospects for attaining the high vortex densities necessary to emulate the fractional quantum Hall effect. We analytically establish the hydrodynamical behaviour 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.