Hidden vortices and Feynman rule in Bose-Einstein condensates with density-dependent gauge potential

TL;DR

This paper investigates vortex nucleation in Bose-Einstein condensates with density-dependent gauge potentials, revealing hidden vortices, modifying Feynman's rule, and demonstrating vortex formation through nonlinear rotations.

Contribution

It develops an empirical Feynman rule for vortices in BECs with density-dependent gauge potentials and confirms it through numerical simulations across different trap geometries.

Findings

Visible and hidden vortices are generated in double-well BECs.

The modified Feynman rule accurately predicts vortex numbers.

Vortices can nucleate via nonlinear rotations without trap rotation.

Abstract

In this article, we numerically investigate the vortex nucleation in a Bose-Einstein condensate trapped in a double-well potential and subjected to a density-dependent gauge potential. A rotating Bose-Einstein condensate, when confined in a double-well potential, not only gives rise to visible vortices but also produces hidden vortices. We have empirically developed the Feynmans rule for the number of vortices versus angular momentum in Bose-Einstein condensates in presence of the density dependent-gauge potentials. The variation of the average angular momentum with the number of vortices is also sensitive to the nature of the nonlinear rotation due to the density-dependent gauge potentials. The empirical result agrees well with the numerical simulations and the connection is verified by means of curve fitting analysis. The modified Feynman rule is further confirmed for the BECs confined in harmonic and toroidal traps. In addition, we show the nucleation of vortices in double-well and toroidally confined Bose-Einstein condensates solely through nonlinear rotations (without any trap rotation) arising through the density dependent-gauge potential.