Two-dimensional quantum droplets in quadrupolar Bose–Einstein condensates

The discovery of stable quantum droplets in dipolar Bose–Einstein condensates has spurred interest in exploring their existence in other polar Bose–Einstein condensates systems. Among these, quadrupolar Bose–Einstein condensates—known for their unique anisotropic interactions—hold strong potential for the emergence of quantum droplets. In this study, we investigate the existence and stability of two-dimensional quantum droplets in systems with electric quadrupole–quadrupole interactions, supplemented by Lee–Huang–Yang quantum corrections. These systems exhibit anisotropic behavior, with droplets that elongate along the polarization axis due to the interplay of quadrupolar interactions and quantum fluctuations, as described by a two-dimensional extended Gross–Pitaevskii equation. Using theoretical analysis and numerical simulations, we demonstrate the stable existence of both fundamental and vortex quantum droplets (with topological charge $S=1$). Key parameters such as peak density, chemical potential, and effective area are examined to elucidate the characteristics of these quantum droplets. Furthermore, we examine collision dynamics under both transverse and longitudinal configurations, shedding light on the anisotropic nature of droplet interactions. These findings pave the way for experimental realization and enrich the theoretical understanding of quantum droplets in quadrupolar Bose–Einstein condensates.