Sound-vortex conversion on droplets: Unraveling acoustic quantum vortices for vortex energy analysis

Vortices—a universal motion form with analogous rotational traits—exist in both quantum fluids (e.g., superfluid helium, Bose–Einstein condensates) and classical fluids (e.g., water). However, current theories explain quantum and classical vortices in isolation (via quantum mechanics and classical fluid mechanics, respectively), creating a gap in understanding their shared energy features. To address the core question “Do vortices have common energy characteristics transcending quantum and classical theories?” this study provides rigorous experimental and theoretical evidence: energy quantization (a core quantum trait) emerges in sound-excited water vortices (classical vortices) at the micrometer-to-millimeter scale. This energy quantization modulates the adjacent microfluidic environment, endowing acoustic vortices with topological robustness and driving two typical collision modes (“head-to-head” and “side-by-side”). Notably, this quantum-like behavior in classical water-based vortices is independent of quantum mechanical mechanisms. The study establishes a top-down vortex energy analysis approach, which interprets the energy of vortices within the host field using the intrinsic angular momentum constraint of the entire host fields. Critically, the intrinsic irrotational nature of these fields may consistently endow the vortices they generate—whether quantum or classical—with three shared characteristics: energy quantization, topological robustness, and hydrodynamic entanglement.