Resonant metasurfaces for generating complex quantum states.

Quantum state engineering, the cornerstone of quantum photonic technologies, mainly relies on spontaneous parametric downconversion and four-wave mixing, where one or two pump photons spontaneously decay into a photon pair. Both of these nonlinear effects require momentum conservation for the participating photons, which strongly limits the versatility of the resulting quantum states. Nonlinear metasurfaces have subwavelength thickness and allow the relaxation of this constraint; when combined with resonances, they greatly expand the possibilities of quantum state engineering. Here, we generated entangled photons via spontaneous parametric downconversion in semiconductor metasurfaces with high-quality factor, quasi-bound state in the continuum resonances. By enhancing the quantum vacuum field, our metasurfaces boost the emission of nondegenerate entangled photons within multiple narrow resonance bands and over a wide spectral range. A single resonance or several resonances in the same sample, pumped at multiple wavelengths, can generate multifrequency quantum states, including cluster states. These features reveal metasurfaces as versatile sources of complex states for quantum information.