Two-Pulse Propagation in a Partially Phase-Coherent Medium

TL;DR

This paper investigates how partial phase coherence in a three-level medium affects two-pulse propagation, revealing that dark state population is limited and that self-induced transparency dominates over EIT in such conditions.

Contribution

It provides analytic and numerical solutions for two-pulse propagation in partially phase-coherent media, extending understanding beyond fully coherent or incoherent models.

Findings

Dark state cannot be fully populated with partial coherence

Self induced transparency dominates over EIT in partially coherent media

A three-level area theorem is suggested for these conditions

Abstract

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.