Robust Vortex Lines, Vortex Rings and Hopfions in 3D Bose-Einstein Condensates

TL;DR

This paper demonstrates the stability and dynamics of vortex lines, rings, and hopfions in 3D Bose-Einstein condensates through spectral analysis and simulations, revealing their robustness and particle-like behavior.

Contribution

It shows that hopfions can be stabilized in simple traps without rotation or inhomogeneous interactions, a novel finding in BEC research.

Findings

Vortex structures are robust over large parameter ranges.

Hopfions can be stabilized without complex trapping methods.

Unstable modes and dynamics are characterized in detail.

Abstract

Performing a systematic Bogoliubov-de Gennes spectral analysis, we illustrate that stationary vortex lines, vortex rings and more exotic states, such as hopfions, are robust in three-dimensional atomic Bose-Einstein condensates, for large parameter intervals. Importantly, we find that the hopfion can be stabilized in a simple parabolic trap, without the need for trap rotation or inhomogeneous interactions. We supplement our spectral analysis by studying the dynamics of such stationary states; we find them to be robust against significant perturbations of the initial state. In the unstable regimes, we not only identify the unstable mode, such as a quadrupolar or hexapolar mode, but we also observe the corresponding instability dynamics. Furthermore, deep in the Thomas-Fermi regime, we investigate the particle-like behavior of vortex rings and hopfions.