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 lineshape. In doing this, 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 refocuses towards the back of the cloud for red detuning. For these regimes, we show which `mean-field' frameworks accurately describe the differing photon scattering lineshapes. Finally, for even denser clouds, mean field models become inaccurate and necessitate the full point dipole model that includes atom-atom correlations.