Binary-vortex quantum droplets

The Lee-Huang-Yang(LHY) correction to the mean field dynamics, originated from quantum fluctuations, can suppress the collapse and create stable localized modes in two and three dimensional systems. Binary quantum droplets(QDs) are studied in free space by introducing the effect of Lee-Huang-Yang correction to the mean field dynamics. Three types of binary QDs are studied, one is belonging to the ground state and the other two are belonging to excited states. In the ground state, the shape change of QDs is demonstrated. Two types of semi-vortex(SV) quantum droplets, one with a bell-shaped fundamental component and the other with the ring-shaped fundamental component, are found in the semi-vortex system. Their characteristics depends on their total norms N, embedded vorticity(topological charge) S and coupling constant g. A noticeable finding is that the SV QDs can be stable up to S = 8. It is found that the size of the quantum droplets depends only on the total norms N, while the inner radii of the vortex component depend only on the embedded vorticity S. The relative share of the total norms of each component with different S is also demonstrated. The stability boundary of the SV QDs are given by the long time evolution. It is found that the SV QDs with the bell-shaped fundamental component are easier to table in relevant small N, while the SV QDs with ring-shaped fundamental components need more large total norms to be stabled. It should be noted that there is a bistable area for these two kinds of SV QDs in the parameter plane of (4π/g,N). The binary vortex quantum droplets, with different embedded vorticity S in each component, are also discussed.