Optical linewidth of a low density Fermi-Dirac gas

We study propagation of light in a Fermi-Dirac gas. We analytically obtain the leading density correction to the optical linewidth at zero temperature . This correction is a direct consequence of the quantum statistical correl ations of atomic positions that modify the optical interactions between the atoms at small interatomic separations. The gas exhibits a dramatic line n arrowing already at very low densities.