Yiyin Zheng | Searcharxiv

arXiv2020

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 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.

nlin.PS↗

arXiv2019

Semidiscrete quantum droplets and vortices

We consider a binary bosonic condensate with weak mean-field (MF) residual repulsion, loaded in an array of nearly one-dimensional traps coupled by transverse hopping. With the MF force balanced by the effectively one-dimensional attraction, induced in each trap by the Lee-Hung-Yang correction (produced by quantum fluctuations around the MF state), stable onsite-centered and intersite-centered semi-discrete quantum droplets (QDs) emerge in the array, as fundamental ones and self-trapped vortices, with winding numbers, at least, up to 5, in both tightly-bound and quasi-continuum forms. The application of a relatively strong trapping potential leads to squeezing transitions, which increase the number of sites in fundamental QDs, and eventually replace vortex modes by fundamental or dipole ones. The results provide the first realization of stable semi-discrete vortex QDs, including ones with multiple vorticity.

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