We derive the properties of polaritons in single-Λ and double-Λ 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-Λ 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.
@article{arxiv.0708.1750,
title = {Dark-State Polaritons in Single- and Double-$\Lambda$ Media},
author = {Y. D. Chong and Marin Soljacic},
journal= {arXiv preprint arXiv:0708.1750},
year = {2008}
}