Slow light amplification in a three-level cascade-type system via spontaneously generated coherence and incoherent pumping

By analytically solving the density matrix equations of a three-level atomic system interacting with two coherent laser fields and an incoherent pumping field under steady-state condition, we have derived the expressions for the absorption and dispersion (and thus group index and group velocity), and population difference as a function of the intensity, frequency, polarization and phase parameters of the laser fields. We have demonstrated that the appearance of spontaneously generated coherence-SGC (characterized by the polarization and non-orthogonality of the electric dipole moments) fundamentally changes the atomic optical responses. By adjusting the strength of SGC and/or incoherent pumping rate, the medium can switch between absorption and amplification regimes, between normal dispersion and anomalous dispersion, and thus light propagation in the medium can switch from slow light to fast light and vice versa. In particular, we have also found that in amplification regime the light is slowed down considerably. Amplifying and slowing light also become more efficient as incoherent pumping rate increases. In addition, the presence of the SGC and incoherent pumping field leads to a sensitive dependence of the atomic responses on the relative phase of the laser fields. Namely, the absorption, dispersion, and group index vary periodically with relative phase.