Stable higher-charge vortex droplets governed by quantum fluctuations in three dimensions

We predict the existence, stability and evolutionary dynamics of three-dimensional (3D) fundamental and vortex droplets governed by quantum fluctuations in a mixture of Bose-Einstein condensates (BECs) trapped in a harmonic potential. Two components of BECs with a fixed ratio of atom numbers form together fundamental droplets with a spherical symmetry and vortex tori with different topological charges. Numerical results show that quantum fluctuations prevent the existence of droplets with atom number below a critical value and forbid the size of droplets to decrease to zero. Specifically, we find that fundamental droplets are completely stable in their entire existence domain and the instability region of vortex droplets expands with the growth of topological charge. Yet, the stability region of vortex droplets with charge up to 8 is still broad, which is rare in 3D nonlinear configurations. Our findings are available to quantum-gas experiments, providing new insight into LHY physics in high-dimensional settings.