Light scattering properties beyond weak-field excitation in atomic ensembles

In the study of optical properties of large atomic system, a weak laser driving is often assumed to simplify the system dynamics by linearly coupled equations. Here, we investigate the light scattering properties of atomic ensembles beyond weak-field excitation through the cumulant expansion method. By progressively incorporating higher-order correlations into the steady-state equations, an enhanced accuracy can be achieved in comparison to the exact solutions from solving a full density matrix. Our analysis reveals that, in the regime of weak dipole-dipole interaction (DDI), the first-order expansion yields satisfactory predictions for optical depth, while denser atomic configurations necessitate consideration of higher-order correlations. As the intensity of incident light increases, atom saturation effects become noticeable, giving rise to significant changes in light transparency, energy shift, and decay rate. This saturation phenomenon extends to subradiant atom arrays even under weak driving conditions, leading to substantial deviations from the linear model. Our findings demonstrate the mean-field models as good extensions to linear models as it balances both accuracy and computational complexity. However, the crucial role of higher-order cumulants in large and dense atom systems remains unclear, since it is challenging theoretically owing to the exponentially increasing Hilbert space in such light-matter interacting systems.