Understanding strong cooperative optical responses in dense and cold atomic ensembles is vital for fundamental science and emerging quantum technologies.
Methodologies for characterizing light-induced quantum effects in such systems, however, are still lacking. Here we unambiguously identify significant quantum many-body effects, robust to position fluctuations and strong dipole-dipole interactions, in light scattered from planar atomic ensembles, by comparing full quantum simulations with a semiclassical model neglecting quantum fluctuations. We find pronounced quantum effects at high atomic densities, light close to saturation intensity, and around subradiant resonances. Such conditions also maximize spin-spin correlations and entanglement between atoms, revealing the microscopic origin of light-induced quantum effects. In several regimes of interest, our approximate model reproduces light transmission remarkably well, permitting analysis of otherwise numerically inaccessible large ensembles, in which we observe many-body analogues of resonance power broadening, vacuum Rabi splitting, and significant suppression in cooperative reflection from atomic arrays.