Enhanced generation of non-degenerate photon-pairs in nonlinear metasurfaces.

We reveal a novel regime of photon-pair generation driven by the interplay of multiple bound states in the continuum resonances in nonlinear metasurfaces. This non-degenerate photon-pair generation is derived from the hyperbolic topology of the transverse phase-matching and can enable orders-of-magnitude enhancement of the photon rate and spectral brightness, as compared to the degenerate regime. We show that the entanglement of the photon-pairs can be tuned by varying the pump polarization, which can underpin future advances and applications of ultra-compact quantum light sources.