Semiclassical Phase-Space Dynamics of Emitter Ensembles with Local Dissipation
We establish that permutation-invariant emitter ensembles with local dissipation admit a semiclassical description on the 4D phase space of a single variable-length collective spin, yielding a scalable truncated Wigner approximation (TWA) for ensemble dynamics. The TWA captures nonlinear dynamics and nonclassical signatures without prescribing low-order closures of correlations. We cast a class of spatially extended emitter systems as interacting ensembles tractable in the TWA to show how strong fluctuations shape directionality in cooperative emission from a pumped chain containing tens of thousands of emitters, using a few hundred phase-space variables. Our results offer a unified description of collective dynamics beyond the classical limit for emitter ensembles.