Photon scattering from a cold, Gaussian atom cloud

We study the effect of a weakly driven atomic cloud's polarization distribution on its photon scattering line shape in the limit where the atoms can be treated as stationary and randomly distributed. We find three distinct polarization regimes. First, for dilute clouds, the polarization magnitude is relatively constant. Second, for denser clouds, polarization builds at the front of the cloud for near-resonant light. Third, when the cloud condenses to the point where its dimensions become comparable to the wavelength, light focuses towards the back of the cloud for red detuning. For these regimes, we show which "mean-field" frameworks accurately describe the differing photon-scattering line shapes. Finally, for even denser clouds, mean-field models become inaccurate and necessitate the full point dipole model that includes atom-atom correlations.