Electromagnetically induced transparency in thermal Rydberg atoms: superatom model with finite Doppler broadening

We study the steady optical responses of a cold atomic ensemble driven into the three-level ladder configuration involving a Rydberg state at finite temperatures. By improving the superatom model with thermal movement included, we calculate relevant atomic coherence effects and find that the residual Doppler broadening at the mK-K temperatures will weaken the nonclassical properties of transmitted probe photons. Furthermore, propagation directions of the probe and coupling fields have a great influence on various properties related to electromagnetically induced transparency. That is, the residual Doppler effect is more destructive to relevant atomic coherence effects in the co-propagation case but can be partially eliminated in the counter-propagation case.