Empty and filled vortices in squeezed 39K Bose-Bose liquid drops

TL;DR

This work investigates vortex formation in squeezed Bose-Bose quantum droplets of $^{39}$K using three-dimensional density-functional theory with Lee-Huang-Yang corrections. By varying axial confinement strength and rotation, it determines the minimal atom number $N_{cv}$ required for stable vortex states and distinguishes between empty (core-empty) and filled (core-filled) vortices as the ground state. The study finds that squeezing and rotation significantly lower $N_{cv}$, with empty vortices prevalent at smaller $N$ and slower rotation, while larger droplets and faster rotation favor filled vortices; multivortex stability remains elusive in the 3D model. These predictions, including lifetimes extended by vortex states despite three-body losses, are within experimental reach and provide guidance for observing vortices in ultradilute quantum droplets.

Abstract

Using density functional theory, we have theoretically studied the formation and the stability of vortices in quantum liquid droplets composed of a mixture of hyperfine states of potassium. Following the experimental setup that produced quantum droplets for the first time, we work with squeezed drops that are compressed in one direction. By squeezing the drops even more, towards a quasi-two dimensional geometry, we study the minimum atom number able to show a stable vortex and obtain that this number is significantly smaller than previous predictions for spherical droplets. The reduction of the critical atom number for forming a stable vortex could make their experimental observation in these droplets, which is still lacking, more feasible. Contrary to results obtained in heteronuclear mixtures, where the energetically preferred vortices are partially filled with the species not participating in the rotation, our results show a relevant stability island of fully empty vortices. Increasing the number of particles in the drop and the speed of rotation, we estimate the transition line between empty and filled vortices.

Figures (8)

• Figure 1: Energy per atom as a function of the number of atoms $N$ for droplets at magnetic field $B = 56.337$ G ($\delta a = -5.536\, a_0$) at squeezing $f=0.25$, plotted for (a) non-rotating droplets and droplets rotating at (b) $10\times 2\pi$ Hz and (c) $20\times 2\pi$ Hz. $VF$ denotes a vortex-free droplet, while $V1$ and $V2$ denote vortices in the first and second components, respectively, and $V12$ denotes 2 vortices, one in each component.
• Figure 2: Total density $\rho(x,0,0)$ profiles along the line passing through the center for a droplet with a vortex in component 2 ($V2$). Droplets are made up from $N=600000$ atoms, and are rotating with angular velocity $\Omega = 20 \times 2\pi$ Hz. (a) Plotted at magnetic field $B = 56.337$ G and three different squeezings, $f=$ 0.25, 0.50, and 0.75. (b) Plotted at different magnetic fields, at squeezing $f=0.25$. All $a_{11}$ units correspond to the field $B=56.337$ ($\delta a = -5.536\, a_0$).
• Figure 3: 2D total density profile in the plane passing through the center for a droplet with a vortex in component 2. The droplet is made up from $N=600000$ atoms at magnetic field $B = 56.337$ G ($\delta a = -5.536\, a_0$) and squeezing $f=0.25$. The droplet is rotating with angular velocity $\Omega = 20 \times 2\pi$ Hz.
• Figure 4: Total density profiles along the line passing through the center for a droplet made up from $N=600000$ atoms at magnetic field $B = 56.337$ G ($\delta a = -5.536\, a_0$) and squeezing $f=0.25$. The droplet is rotating with angular velocity $\Omega = 20 \times 2\pi$ Hz. $VF$ denotes a vortex-free droplet, while $V1$ and $V2$ denote vortices in the centers of the first and second components, respectively, and $V12$ denotes 2 vortices, one in each component.
• Figure 5: Critical number of atoms for hosting a vortex, $N_{cv}$, as a function of angular velocity $\Omega$, for a droplet at three magnetic fields $B = 56.337$ G, $B = 56.453$ G and $B = 56.574$ G, at squeezing $f=0.25$.