Two-pulse propagation in a partially phase-coherent medium

We analyze the effects of partial coherence of ground-state preparation on two-pulse propagation in a three-level Lambda medium, in contrast to previous treatments that have considered the cases of media whose ground states are characterized by probabilities (level populations) or by probability amplitudes (coherent pure states). We present analytic solutions of the Maxwell-Bloch equations, and we extend our analysis with numerical solutions to the same equations. We interpret these solutions in the bright and dark dressed-state basis, and show that they describe a population transfer between the bright and dark state. For mixed-state Lambda media with partial ground-state phase coherence the dark state can never be fully populated. This has implications for phase-coherent effects such as pulse matching, coherent population trapping, and electromagnetically induced transparency (EIT). We show that for partially phase-coherent three-level media, self-induced transparency dominates EIT and our results suggest a corresponding three-level area theorem.