Directional emission of down-converted photons from a dielectric nanoresonator

Creation of correlated photon pairs is one the key topics in contemporary quantum optics. Here, we theoretically describe generation process spontaneous parametric down-conversion a resonant spherical nanoparticle made dielectric material with bulk $\chi^{(2)}$ nonlinearity. We pick size that satisfies condition eigenmodes described by Mie theory. reveal highly directional photon-pair can be observed utilising nonlinear Kerker-type effect, and this regime provides useful polarisation correlations.