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Quantum state engineering, the cornerstone of quantum photonic technologies,mainly relies on spontaneous parametric down-conversion and four-wave mixing,where one or two pump photons decay into a photon pair. Both these nonlineareffects require momentum conservation (i.e., phase-matching) for theparticipating photons, which strongly limits the versatility of the resultingquantum states. Nonlinear metasurfaces, due to their subwavelength thickness,relax this constraint and extend the boundaries of quantum state engineering.Here, we generate entangled photons via spontaneous parametric down-conversionin semiconductor metasurfaces with high-quality resonances. By enhancing thequantum vacuum field, our metasurfaces boost the emission of photon pairswithin narrow resonance bands at multiple selected wavelengths. Due to therelaxed momentum conservation, the same resonances support photon pairgeneration from pump photons of practically any energy. This enables thegeneration of complex frequency-multiplexed quantum states, in particularcluster states. Our results demonstrate the multifunctional use of metasurfacesfor quantum state engineering.

Resonant Semiconductor Metasurfaces for Generating Complex Quantum States