Electromagnetically-induced-transparency-based paired photon generation

We describe the theory of paired photon generation in a double-Λ atomic system. Using the Heisenberg-Langevin formalism we evaluate and analyze the spectral generation rates and intensity correlation function for the output fields. Different regimes of parametric down conversion are analyzed. We discuss the influence of the optical depth and Langevin noise fluctuations on the paired photon generation and predict that at the optical depth of 100 or more the contribution of Langevin noise fluctuations is small and therefore Stokes and anti-Stokes photons are generated mostly in pairs. Comparison between the theory and experiments shows good agreement