Dispersion of the dielectric permittivity of dense and ultracold atomic   gases
  On the basis of general theoretical results developed previously in JETP 112, 246 (2011) we analyze the atomic polarization created by weak monochromatic light in an optically thick, dense and cold atomic ensemble. We show that the amplitude of the polarization averaged over a uniform random atomic distribution decreases exponentially beyond the boundary regions. The phase of this polarization increases linearly with increasing penetration into the medium. On these grounds, we determine numerically the wavelength of the light in the dense atomic medium, its extinction coefficient, and the complex refractive index and dielectric constant of the medium. The dispersion of the permittivity is investigated for different atomic densities. It is shown that for dense clouds, the real part of the permittivity is negative in some spectral domains. 
Ya. A. Fofanov, A. S. Kuraptsev, I. M. Sokolov and M.D. Havey
quant-ph physics.atm-clus