Two-Pulse Propagation in Media with Quantum-Mixed Ground States

TL;DR

This paper investigates two-pulse propagation in lambda-type media with quantum-mixed ground states, extending the Area Theorem to unify various phenomena like EIT and SRS, supported by numerical and analytic solutions.

Contribution

It extends the Area Theorem for two-pulse propagation to include complex scenarios such as EIT and SRS in media with quantum-mixed ground states, with comprehensive numerical and analytic analysis.

Findings

Extended Area Theorem unifies two-pulse propagation scenarios.

Large one-photon detuning affects pulse Area reliability.

Numerical solutions reveal features of pulse-medium interactions.

Abstract

We examine fully coherent two-pulse propagation in a lambda-type medium, under two-photon resonance conditions and including inhomogeneous broadening. We examine both the effects of short pulse preparation and the effects of medium preparation. We contrast cases in which the two pulses have matched envelopes or not, and contrast cases in which ground state coherence is present or not. We find that an extended interpretation of the Area Theorem for single-pulse self-induced transparency (SIT) is able to unify two-pulse propagation scenarios, including some aspects of electromagnetically-induced transparency (EIT) and stimulated Raman scattering (SRS). We present numerical solutions of both three-level and adiabatically reduced two-level density matrix equations and Maxwell's equations, and show that many features of the solutions are quickly interpreted with the aid of analytic solutions that we also provide for restricted cases of pulse shapes and preparation of the medium. In the limit of large one-photon detuning, we show that the two-level equations commonly used are not reliable for pulse Areas in the 2$\pi$ range, which allows puzzling features of previous numerical work to be understood.