Dark-State Polaritons in Single- and Double-$\Lambda$ Media

TL;DR

This paper derives the properties of dark-state polaritons in single- and double-$\Lambda$ media, demonstrating their potential for quantum frequency conversion while maintaining coherence, with analysis based on a microscopic eigenvalue approach.

Contribution

It provides a microscopic derivation of polariton properties in $\Lambda$ media and shows how double-$\Lambda$ systems enable coherent photon up- and down-conversion.

Findings

Double-$\Lambda$ media can convert single photons while preserving quantum coherence.

Dark-state polaritons protect quantum effects against decay.

Conversion efficiency depends on sample size and metastable state lifetime.

Abstract

We derive the properties of polaritons in single-$\Lambda$ and double-$\Lambda$ media using a microscopic equation-of-motion technique. In each case, the polaritonic dispersion relation and composition arise from a matrix eigenvalue problem for arbitrary control field strengths. We show that the double-$\Lambda$ medium can be used to up- or down-convert single photons while preserving quantum coherence. The existence of a dark-state polariton protects this single-photon four-wave mixing effect against incoherent decay of the excited atomic states. The efficiency of this conversion is limited mainly by the sample size and the lifetime of the metastable state.