Quantum droplets in two-dimensional optical lattices

TL;DR

This paper investigates the stability and properties of quantum droplets in two-dimensional optical lattices, revealing stability conditions, degeneracy of vortex states, and violations of traditional stability criteria.

Contribution

It introduces a detailed analysis of onsite and offsite quantum droplets in 2D lattices, including stability regions and the impact of vorticity on degeneracy and stability.

Findings

Stable regions for different quantum droplet configurations identified.

Vakhitov-Kolokolov criterion can be violated in these systems.

Degeneracy observed among vortex quantum droplets with the same number of sites.

Abstract

We study the stability of zero-vorticity and vortex lattice quantum droplets (LQDs), which are described by a two-dimensional (2D) Gross-Pitaevskii (GP) equation with a periodic potential and Lee-Huang-Yang (LHY) term. The LQDs are divided in two types: onsite-centered and offsitecentered LQDs, the centers of which are located at the minimum and the maximum of the potential, respectively. The stability areas of these two types of LQDs with different number of sites for zerovorticity and vorticity with S = 1 are given. We found that the u-N relationship of the stable LQDs with a fixed number of sites can violate the Vakhitov-Kolokolov (VK) criterion, which is a necessary stability condition for nonlinear modes with an attractive interaction. Moreover, the u-N relationship shows that two types of vortex LQDs with the same number of sites are degenerated, while the zero-vorticity LQDs are not degenerated. It is worth mentioning that the offsite-centered LQDs with zero-vorticity and vortex LQDs with S = 1 are heterogeneous.