Quantum nonlinear light emission in metamaterials: broadband Purcell enhancement of parametric downconversion

Single-photon and correlated two-photon sources are important elements for optical information systems. Nonlinear downconversion light sources are robust and stable emitters of single photons and entangled photon pairs. However, the rate of downconverted light emission, dictated by the properties of low-symmetry nonlinear crystals, is typically very small, leading to significant constrains in device design and integration. In this Letter, we study principles of spontaneous emission control (i.e. Purcell effect) generalized to describe the enhancement of nonlinear generation of quantum light through spontaneous parametric downconversion. We develop a theoretical framework, based on eigen-mode analysis, to study quantum nonlinear emission in a general anisotropic, dispersive and lossy media. Our theory provides an unprecedented insight into the emission process. We find that spontaneous parametric downconversion in a media with hyperbolic dispersion is broadband and phase-mismatch-free. We further predict a 1000-fold enhancement of the downconverted emission rate with up to 105 photon pairs per second in experimentally realistic nanostructures. Our theoretical formalism and approach to Purcell enhancement of nonlinear optical processes, provides a framework for description of quantum nonlinear optical phenomena in complex nanophotonic structures.