A numerical study of vortex nucleation in 2D rotating Bose-Einstein condensates

TL;DR

This paper presents a new numerical method for studying vortex structures in rotating Bose-Einstein condensates, capable of handling various regimes and providing detailed vortex analysis.

Contribution

The paper introduces a novel numerical approach for energy minimization in multicomponent BECs, including vortex and vortex sheet analysis, validated against existing methods.

Findings

Efficient computation of vortex indices in BECs

Validation of theoretical vortex structures

Comparison with existing numerical methods

Abstract

This article introduces a new numerical method for the minimization under constraints of a discrete energy modeling multicomponents rotating Bose-Einstein condensates in the regime of strong confinement and with rotation. Moreover, we consider both segregation and coexistence regimes between the components. The method includes a discretization of a continuous energy in space dimension 2 and a gradient algorithm with adaptive time step and projection for the minimization. It is well known that, depending on the regime, the minimizers may display different structures, sometimes with vorticity (from singly quantized vortices, to vortex sheets and giant holes). In order to study numerically the structures of the minimizers, we introduce in this paper a numerical algorithm for the computation of the indices of the vortices, as well as an algorithm for the computation of the indices of vortex sheets. Several computations are carried out, to illustrate the efficiency of the method, to cover different physical cases, to validate recent theoretical results as well as to support conjectures. Moreover, we compare this method with an alternative method from the literature.