Vortex-ring quantum droplets in a radially-periodic potential

Abstract

We establish stability and characteristics of two-dimensional (2D) vortex ring-shaped quantum droplets (QDs) formed by binary Bose-Einstein condensates (BECs). The system is modeled by the Gross-Pitaevskii (GP) equation with the cubic term multiplied by a logarithmic factor (as produced by the Lee-Huang-Yang correction to the mean-field theory) and a potential which is a periodic function of the radial coordinate. Narrow vortex rings with high values of the topological charge, trapped in particular circular troughs of the radial potential, are produced. These results suggest an experimentally relevant method for the creation of vortical QDs (thus far, only zero-vorticity ones have been reported). The 2D GP equation for the narrow rings is approximately reduced to the 1D form, which makes it possible to study the modulational stability of the rings against azimuthal perturbations. Full stability areas are delineated for these modes. The trapping capacity of the circular troughs is identified for the vortex rings with different winding numbers (WNs). Stable compound states in the form of mutually nested concentric multiple rings are constructed too, including ones with opposite signs of the WNs. Other robust compound states combine a modulationally stable narrow ring in one circular potential trough and an azimuthal soliton performing orbital motion in an adjacent one. The results may be used to design a device employing coexisting ring-shaped modes with different WNs for data storage.

Two-dimensional quantum droplets in binary quadrupolar condensates

“…The possibility for the stabilization of the vortex modes has been revealed by studies of BEC systems under the action of spatially periodic and quasiperiodic lattice potentials [65][66][67][68][69][70][71][72][73][74][75][76][77]. Recently, stable QDs in 2D square lattices [78] and ring-shaped QDs with explicit and hidden vorticity in a radially periodic potential [79,80] have been predicted ('hidden vorticity' means as a vortex-antivortex bound state in a two-component system with zero total angular momentum [74]). In the free space, stable 2D matter-wave solitons were predicted in microwave-coupled binary condensates [81], and solutions for stable semi-vortices, i.e.…”