Identification of vortices in quantum fluids: finite element algorithms and programs

TL;DR

This paper introduces finite-element algorithms and a free software toolbox for accurately identifying and analyzing vortices in quantum fluids like Bose-Einstein condensates and superfluid helium, validated with numerical and experimental data.

Contribution

The paper presents a novel, validated finite-element based toolbox for vortex detection in quantum fluids, applicable to both numerical simulations and experimental images.

Findings

Robust vortex detection in 2D and 3D quantum fluids

Accurate vortex radius and lattice parameter estimation

Effective analysis of experimental and numerical data

Abstract

We present finite-element numerical algorithms for the identification of vortices in quantum fluids described by a macroscopic complex wave function. Their implementation using the free software FreeFem++ is distributed with this paper as a post-processing toolbox that can be used to analyse numerical or experimental data. Applications for Bose-Einstein condensates (BEC) and superfluid helium flows are presented. Programs are tested and validated using either numerical data obtained by solving the Gross-Pitaevskii equation or experimental images of rotating BEC. Vortex positions are computed as topological defects (zeros) of the wave function when numerical data are used. For experimental images, we compute vortex positions as local minima of the atomic density, extracted after a simple image processing. Once vortex centers are identified, we use a fit with a Gaussian to precisely estimate vortex radius. For vortex lattices, the lattice parameter (inter-vortex distance) is also computed. The post-processing toolbox offers a complete description of vortex configurations in superfluids. Tests for two-dimensional (giant vortex in rotating BEC, Abrikosov vortex lattice in experimental BEC) and three-dimensional (vortex rings, Kelvin waves and quantum turbulence fields in superfluid helium) configurations show the robustness of the software. The communication with programs providing the numerical or experimental wave function field is simple and intuitive. The post-processing toolbox can be also applied for the identification of vortices in superconductors.