Full Quantum Theory of Transient-State Electromagnetically Induced Transparency

We develop a full quantum theory of transient-state electromagnetically induced transparency (EIT) in the vapor of three-level $\Lambda$-type atoms interacting with probe and coupling lasers. As applications of the full quantum theory, we show that transient-state EIT medium exhibits normal dispersion and find that group velocities of both coupling and probe lasers are greatly reduced. It is shown that the group velocity of the probe laser in the transient-state EIT case is equal to that in the adiabatic EIT case and that the coupling laser group velocity in the transient-state EIT is generally less than that in the adiabatic EIT.