Effect of relaxation rate on population distribution, EIT and refraction in \varLambda and V systems

In the three-level Λ-type and V-type systems, we find that the same pump-effect parameter R(=\frac2|V_c|^2\gamma(\omega_ac-\omega_c)^2+\gamma^2) determines the population distributions, while the probe field leads to population fluctuations near the absorption peaks. With the increasing of the relaxation rate \gamma, the population distributions are shifted and their fluctuation amplitudes decrease. At the same time the electromagnetically induced transparency window becomes a broadened absorption peak, and the dispersion at the zero probe detuning changes from positive to negative. Large population fluctuation and non-fluctuation observed in different systems are attributed to the different relaxation rates.