We analyze the temporal response of the fluorescence light that is emitted from a dense gas of cold atoms driven by a laser. When the average interatomic distance is smaller than the wavelength of the photons scattered by the atoms, the system exhibits strong dipolar interactions and collective dissipation. We solve the exact dynamics of small systems with different geometries and show how these collective features are manifest in the scattered light properties such as the photon emission rate, the power spectrum and the second-order correlation function. By calculating these quantities beyond the weak driving limit, we make progress in understanding the signatures of collective behavior in these many-body systems. Furthermore, we clarify the role of disorder on the resonance fluorescence, of direct relevance for recent experimental efforts that aim at the exploration of many-body effects in dipole-dipole interacting gases of atoms.
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