Refractive index of a single atom experienced by a single photon

The propagation of quantum field interacting with a single two-level atom has been studied. Using the Gaussian quantum mode functions, we calculate evolution of the quantum state that includes atomic and field variable. We demonstrated the phase and group velocities of the single photon propagation that can be of great importance for long quantum communications. The results can be used for controlling quantum field propagation, and for design of optical elements such as a quantum prism and a quantum lens.