Nonlinear optical properties of an electromagnetically-induced-transparency medium interacting with two quantized fields

We study linear and nonlinear optical properties of electromagnetically induced transparency (EIT) medium interacting with two quantized laser fields for adiabatic EIT case. We show that EIT medium exhibits normal dispersion. Kerr and higher order nonlinear refractive-index coefficients are also calculated in a completely analytical form. It is indicated that EIT medium exhibits giant resonantly enhanced nonlinearities. We discuss the response of the EIT medium to nonclassical light fields and find that the polarization vanishes when the probe laser is initially in a nonclassical state of no single-photon coherence.