Hopfions in the Lee-Huang-Yang superfluids

TL;DR

This paper explores the existence, stability, and properties of hopfion topological states in Lee-Huang-Yang superfluids, revealing stable configurations with specific topological numbers and potential for experimental realization.

Contribution

It systematically investigates hopfion states in LHY superfluids, highlighting their stability conditions, topological features, and dependence on physical parameters, which was not previously detailed.

Findings

Stable hopfions with s=1 and m=0 to 4 exist under certain conditions.

Hopfions exhibit distinct topological phase distributions and size scaling with chemical potential.

Stable hopfions are experimentally accessible in current BEC setups.

Abstract

It is known that, under appropriate conditions, mean-field interactions can be canceled in binary BEC, leading to the formation of the Lee-Huang-Yang (LHY) superfluid, in which the nonlinearity is solely represented by the quartic LHY term. In this work we systematically investigate the existence, stability and evolution of hopfion states in this species of quantum matter. They are characterized by two independent topological winding numbers: inner twist $s$ of the vortex-ring core and overall vorticity $m$. The interplay between the LHY self-repulsion and a trapping harmonic-oscillator potential results in stability of the hopfions with $s = 1$ and $m$ ranging from $0$ to $4$. The hopfions exhibit distinct topological phase distributions along the vertical axis and the radial direction in the horizontal plane. Their effective radius and peak density increase with the chemical potential, along with expansion of the vortex-ring core. Although the instability domain of the hopfion modes broadens with the increase of $m$, stable hopfions persist in a wide range of the chemical potential, up to $m=4$, at least, provided that the norm exceeds a certain threshold value. The predictions are experimentally accessible in currently used BEC setups.