Quantum droplets in two-dimensional optical lattices

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 offsite-centered 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 zero-vorticity and vorticity with S = 1 are given. We found that the mu -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 mu -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.

Automated summary

We studied the stability of zero-vorticity and vortex lattice quantum droplets described by a 2D GP equation, finding the stability areas for different numbers of sites and vorticities. The relationship between mu and N for stable LQDs may violate the VK criterion, and two types of vortex LQDs with the same number of sites were found to be degenerate, while zero-vorticity LQDs were not. The offsite-centered LQDs with zero-vorticity and vortex LQDs with S = 1 were heterogeneous.