Static and dynamical properties of quadrupolar quantum droplets in quasi-2D condensates

Quantum droplets, stabilized by beyond-mean-field effects, represent a novel and intriguing state of matter in quantum many-body systems. While previous studies have focused primarily on dipolar and contact-interacting systems, quadrupolar condensates remain relatively unexplored. In this work, we explore the formation, structural properties, and dynamical behaviors of quantum droplets in a two-component quadrupolar Bose–Einstein condensate confined to a quasi-two-dimensional geometry. By incorporating quadrupole–quadrupole interactions (QQIs) and Lee–Huang–Yang (LHY) corrections into an extended Gross–Pitaevskii equation, we systematically study both ground-state and vortex-state droplets. Analytical results obtained via the Thomas–Fermi approximation predict flat-topped density profiles and linear scaling between effective area and particle number. These predictions are corroborated by numerical simulations, which also reveal the saturation of peak density and chemical potential at large norm. Furthermore, vortex quantum droplets exhibit anisotropic elliptical morphologies due to the directional nature of QQIs, with their aspect ratios significantly tunable by varying the particle number and quadrupolar interaction strength. Collision dynamics demonstrate rich behavior modulated by velocity and topology: ground-state droplets transition from inelastic merging to quasi-elastic scattering and quantum penetration, while vortex droplets exhibit phase-induced repulsion, fragmentation, and topologically protected tunneling. These findings offer a comprehensive understanding of how higher-order interactions and quantum fluctuations govern the formation and stability of quadrupolar droplets. This work lays a theoretical foundation for experimental realization and opens new directions for exploring anisotropic quantum fluids, topological excitations, and applications in quantum sensing and simulation.