Theory of parametric frequency down conversion of light

TLDR

The study examines parametric frequency down‑conversion, where pump photons in a nonlinear crystal spontaneously split into lower‑frequency signal and idler photons, with the resulting fields quantized across a continuum of modes. The authors aim to compare these theoretical predictions with recent experimental results. They find that, when detectors are positioned to receive conjugate signal and idler photons, the two‑photon detection probability can equal the single‑photon probability, and that the time correlation of the detected photons is limited only by detector resolution or down‑converted bandwidth, independent of pump coherence or crystal length.

Abstract

A theoretical study is made of the process in which incident pump photons that interact with a nonlinear medium (such as a crystal lacking inversion symmetry) are spontaneously split into lower-frequency signal and idler photons. The down-converted fields are quantized and described by a continuum of modes, a subset of which interacts with each photodetector. It is shown that when two ideal photodetectors are appropriately located so that they receive the conjugate signal and idler photons, then the joint probability of two-photon detection by the two detectors can equal the single-photon detection probability. The time correlation between the two detected photons is shown to be limited either by the resolving time of the detectors, or by the bandwidth of the down-converted light, and to be independent of the coherence time of the pump field or of the length of the nonlinear medium. These conclusions are compared with the results of recent experiments.