Elongated vortex quantum droplets in binary Bose-Einstein condensates

TL;DR

This paper demonstrates the creation and stability analysis of elongated vortex quantum droplets in binary Bose-Einstein condensates using spatially modulated inter-species interactions, revealing stable vortex states and dynamic behaviors.

Contribution

It introduces a method to stabilize elongated vortex quantum droplets via Gaussian-shaped inter-species interaction modulation in BECs, including analysis of stability and collision dynamics.

Findings

Stable elongated QDs with vorticity S=0 achieved.

Partly stable vortex QDs with S=1,2,3,4 identified.

Collisions can merge QDs into breathing states or cause quasi-elastic interactions.

Abstract

Stability of elongated (``slender") quantum droplets (QDs) with embedded unitary and multiple vorticity is a problem that was not solved previously. In this work, we propose a solution which relies upon the use of the spatial modulation of the inter-species scattering length in the binary Bose-Einstein condensates, in the form of a two-dimensional axisymmetric Gaussian, shaped by means of the optical Feshbach resonance. The corresponding effective nonlinear trapping potential supports completely stable elongated QDs with vorticity $S=0$ and partly stable families of elongated QDs with $S=1,2,3,4$ (other nonlinear systems do not maintain stability of vortex droplets with $\geq 2$). We systematically analyze effects of the amplitude and width of the Gaussian modulation, as well as the total number of atoms, on the shape and stability of the QDs, some effects being explained analytically. Collisions between identical QDs with $% S=1$ moving in opposite directions along the central axis leads to their merger into still more elongated breathing QDs with the same vorticity, while collisions between QDs with $S=\pm 1$ are quasi-elastic. Moving modulation profiles are able to adiabatically rotate the trapped elongated QDs. Application of a torque to the vector QD sets in the gyroscopic regime of robust precession, which realizes a macroscopic spin-orbit-coupling effect.