  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 treastments 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/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 (SIT) dominates EIT and our results suggest a corresponding
three-level area theorem.
