Amplification without inversion and high refractive index in heterogeneous molecules

The system of interest is a closed three-level V-type system with two excited near degenerated levels in a weak probe field and a strong coupling field, in the presence of an incoherent pumping field. We investigate analytically the conditions to have amplification without population inversion or high index of refraction without absorption due to spontaneously generated coherence and incoherent pumping. The perturbation solution of the density matrix equation in the steady state case is derived. We find that the refractive index and absorption coefficient have a periodic dependence on the relative phase of the probe and coupling fields. The relative phase values for which the system exhibits a high refractive index without absorption are obtained. The conditions on incoherent pumping rate related to that for the angle between the two transition dipole moments and spontaneous emission rates of the two excited states to obtain the probe field gain without population inversion are derived. We propose a three-level V-type system with spontaneously generated coherence from LiH molecule which can achieve quasi-high index of refraction without absorption and amplification without population inversion.