# Quasi-stable quantum vortex knots and links in anisotropic harmonically trapped Bose-Einstein condensates

## TL;DR

This paper demonstrates the long-time existence of topologically nontrivial quantum vortex knots and links in anisotropic trapped Bose-Einstein condensates through numerical simulations, indicating their potential experimental observability.

## Contribution

It reveals specific parametric conditions under which quantum vortex knots and links remain quasi-stable in anisotropic BECs, a novel finding in the field.

## Key findings

- Vortex knots can persist for hundreds of rotation times near certain trap anisotropies.
- Lifetimes depend on trap anisotropy and initial knot configuration.
- Potential for experimental observation of these quantum vortex structures.

## Abstract

Long-time existence of topologically nontrivial configurations of quantum vortices in the form of torus knots and links in trapped Bose-Einstein condensates is demonstrated numerically within the three-dimensional Gross-Pitaevskii equation with external anisotropic parabolic potential. We find out parametric domains near the trap anisotropy -- axial over planar frequency trapping ratio $\lambda\approx 1.5-1.6$ where the lifetime of such quasi-stationary rotating vortex structures is many hundreds of typical rotation times. This suggests the potential experimental observability of the structures. We quantify the relevant lifetimes as a function of the model parameters (e.g. $\lambda$) and initial condition parameters of the knot profile.