Universal Two-Excitation Scattering in Two-Dimensional Subwavelength Atomic Arrays

Subwavelength atomic arrays are a leading platform for engineering strong light-matter interactions, presenting exciting opportunities for quantum science. However, a full understanding of their multiexcitation dynamics remains a significant challenge. In this Letter, we uncover a remarkable universal phenomenon that emerges in these arrays. Using scattering theory to analyze two-excitation interactions, we reveal a profound simplification near critical points of the collective atomic excitation band structure, determined solely from single-excitation properties. At these critical points, which emerge as band edges and saddle points (Van Hove singularities) in the two-excitation phase space, scattering becomes universal and the full two-excitation scattering matrix decomposes into a block-diagonal form. Remarkably, all scattering processes involving the photon field are completely suppressed, resulting in the perfect isolation of a unitary, nonlinear interaction channel between collective dark spin waves. Our findings provide exact analytical insights into few-body nonlinearities and establish a universal framework for analyzing complex scattering phenomena in ordered atomic systems.