  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.
