Two-dimensional vortex quantum droplets

TL;DR

This paper constructs and analyzes stable two-dimensional vortex quantum droplets with vorticity up to 5, revealing their shape, stability conditions, and dynamic behaviors, including collisions and deformations, in a mean-field model with Lee-Huang-Yang correction.

Contribution

It introduces stable 2D vortex quantum droplets with high vorticity, providing systematic numerical and analytical analysis of their stability, shape, and dynamics, which was not previously demonstrated.

Findings

Vortical quantum droplets are stable up to vorticity S=5.

The shape of droplets expands with increasing vorticity and norm.

Stable hidden-vorticity states exist beyond typical model limits.

Abstract

It was recently found that the Lee-Huang-Yang (LHY) correction to the mean-field Hamiltonian suppresses the collapse and creates stable localized modes (two-component "quantum droplets", QDs) in two and three dimensions. We construct two-dimensional\ self-trapped modes in the form of QDs with vorticity $S$ embedded into each component. The QDs feature a flat-top shape, which expands with the increase of $S$ and norm $N$. An essential finding, produced by a systematic numerical analysis and analytical estimates, is that the vortical QDs are \emph{stable} (which is a critical issue for vortex solitons in nonlinear models) up to $S=5$, for $N$ exceeding a certain threshold value. In the condensate of $^{39}$K atoms, in which QDs with $S=0$ and a quasi-2D shape were created recently, the vortical droplets may have radial size $\lesssim 30$ $\mathrm{\mu}$m, with the number of atoms in the range of $10^{4}-10^{5}$. It is worthy to note that \textit{hidden-vorticity} states in QDs with topological charges $% S_{+}=-S_{-}=1$ in its components, which are prone to strong instability in other settings, have their stability region too, although it may be located beyond applicability limits of the underlying model. Dynamics of elliptically deformed QDs, which form rotating elongated patterns or ones with strong oscillations of the eccentricity, as well as collisions of QDs, are also addressed.