Electromagnetically induced transparency of the medium composed of atoms in thermal motion

We investigate electromagnetically induced transparency of a medium composed of N Lambda-type three-level atoms in thermal motion with an initial momentum distribution modelled by a Gaussian function. We treat atomic centre-of-mass motion as an independent degree of freedom and study the dependence of susceptibility on the thermal motion characterized by the width and centre of Gaussian momentum distribution. A larger width does not always lead to larger resonant absorption and if the probe and controlling fields copropagate in the degenerate and resonant cases, transparency can be obtained regardless of the thermal motion of the atoms.