Complete conversion between one and two photons in nonlinear waveguides: Theory of dispersion engineering

High-efficiency photon-pair production is a long-sought-after goal for many optical quantum technologies, and coherent photon conversion (CPC) processes are promising candidates for achieving this. We show theoretically how to control coherent conversion between a narrow-band pump photon and broadband photon pairs in nonlinear optical waveguides by tailoring frequency dispersion for broadband quantum frequency mixing. We reveal that complete deterministic conversion as well as pump-photon revival can be achieved at a finite propagation distance. We also find that high conversion efficiencies can be realised robustly over long propagation distances. These results demonstrate that dispersion engineering is a promising way to tune and optimise the CPC process.