Gauge matters: Observing the vortex-nucleation transition in a Bose condensate

TL;DR

This paper demonstrates how gauge-dependent phase gradients in Bose-Einstein condensates under artificial magnetic fields can be observed through shear in time-of-flight images, revealing the vortex-nucleation transition as a structural phase change.

Contribution

It introduces a macroscopic shear measurement method to detect vortex nucleation in BECs, highlighting the gauge dependence of the order parameter in quantum gases.

Findings

Vortices nucleate above a critical artificial magnetic field strength.

Shear in BEC spatial distribution indicates the vortex transition.

Gauge choice influences the observed shear and transition dynamics.

Abstract

The order parameter of a quantum-coherent many-body system can include a phase degree of freedom, which, in the presence of an electromagnetic field, depends on the choice of gauge. Because of the relationship between the phase gradient and the velocity, time-of-flight measurements reveal this gradient. Here, we make such measurements using initially trapped Bose-Einstein condensates (BECs) subject to an artificial magnetic field. Vortices are nucleated in the BEC for artificial field strengths above a critical value, which represents a structural phase transition. By comparing to superfluid-hydrodynamic and Gross-Pitaevskii calculations, we confirmed that the transition from the vortex-free state gives rise to a shear in the released BEC's spatial distribution, representing a macroscopic method to measure this transition, distinct from direct measurements of vortex entry. Shear is also affected by an artificial electric field accompanying the artificial magnetic field turn-off, which depends on the details of the physical mechanism creating the artificial fields, and implies a natural choice of gauge. Measurements of this kind offer opportunities for studying phase in less-well-understood quantum gas systems.