Geometric phases of a vortex in a superfluid

TL;DR

This paper investigates the geometric phases of vortices in superfluid Bose-Einstein condensates, revealing additional contributions beyond previous predictions and proposing experimental measurement methods.

Contribution

It identifies two new contributions to vortex geometric phases using superfluid electrodynamics, extending prior theoretical results.

Findings

Discovered additional contributions to geometric phase from edge currents and displacement currents.

Resolved apparent discrepancies with earlier predictions.

Proposed experimental setups for measuring vortex geometric phases.

Abstract

We consider geometric phases of mobile quantum vortices in superfluid Bose-Einstein condensates. Haldane and Wu [Phys. Rev. Lett. 55, 2887 (1985)] showed that the geometric phase, $\gamma_{\mathcal C}=2\pi N_{\mathcal C}$, of such a vortex is determined by the number of condensate atoms $N_{\mathcal C}$ enclosed by the vortex trajectory. Considering an experimentally realistic freely orbiting vortex leads to an apparent disagreement with this prediction. We resolve it using the superfluid electrodynamics picture, which allows us to identify two additional contributions to the measured geometric phase; (i) a topologically protected edge current of vortices at the condensate boundary, and (ii) a superfluid displacement current. Our results generalise to, and pave the way for experimental measurements of vortex geometric phases using scalar and spinor Bose--Einstein condensates, and superfluid Fermi gases.