Stable higher-order vortex quantum droplets in an annular potential

TL;DR

This paper investigates the existence and stability of two-dimensional vortex quantum droplets in binary Bose-Einstein condensates within a ring-shaped trap, revealing stable high-vorticity states and analytical insights into their modulational instability.

Contribution

It demonstrates the stability of upper-branch vortex quantum droplets with high topological charge in a ring trap, providing a new method for experimental realization of stable high-vorticity states.

Findings

Upper-branch VQDs are fully stable for all topological charges studied.

Stable VQDs follow the anti-Vakhitov-Kolokolov criterion.

Analytical study of modulational instability in tight radial traps.

Abstract

We address the existence, stability, and evolution of two-dimensional vortex quantum droplets (VQDs) in binary Bose-Einstein condensates trapped in a ring-shaped potential. The interplay of the Lee-Huang-Yang-amended nonlinearity and trapping potential supports two VQD branches, controlled by the radius, width and depth of the potential profile. While the lower-branch VQDs, bifurcating from the system's linear modes, are completely unstable, the upper branch is fully stable for all values of the topological charge $m$ and potential's parameters. Up to $m=12$ (at least), stable VQDs obey the {\it anti-Vakhitov-Kolokolov} criterion. In the limit of an extremely tight radial trap, the modulational instability of the quasi-1D azimuthal VQDs is studied analytically. We thus put forward an effective way to produce stable VQDs with higher vorticity but a relatively small number of atoms, which is favorable for experimental realization.