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Atoms subject to weak coherent incident light can be treated as coupledclassical linear oscillators, supporting subradiant and superradiant collectiveexcitation eigenmodes. We identify the limits of validity of this \emph{linearclassical oscillator model} at increasing intensities of the drive by solvingthe quantum many-body master equation for coherent and incoherent scatteringfrom a chain of trapped atoms. We show that deviations from the linearclassical oscillator model depend sensitively on the resonance linewidths$\upsilon_\alpha$ of the collective eigenmodes excited by light, with theintensity at which substantial deviation occurs scaling as a powerlaw of$\upsilon_\alpha$. The linear classical oscillator model then becomesinaccurate at much lower intensities for subradiant collective excitations thansuperradiant ones, with an example system of seven atoms resulting in criticalincident light intensities differing by a factor of 30 between the two cases.By individually exciting eigenmodes we find that this critical intensity has a$\upsilon_\alpha^{2.5}$ scaling for narrower resonances and more stronglyinteracting systems, while it approaches a $\upsilon_\alpha^3$ scaling forbroader resonances and when the dipole-dipole interactions are reduced. The$\upsilon_\alpha^3$ scaling also corresponds to the semiclassical resultwhereby quantum fluctuations between the atoms have been neglected. We studyboth the case of perfectly mode-matched drives and the case of standing wavedrives, with significant differences between the two cases appearing only atvery subradiant modes and positions of Fano resonances.

Optical response of atom chains beyond the limit of low light intensity: The validity of the linear classical oscillator model