We present a single-photon transduction scheme using four-wave-mixing and quantum scattering in planar, cooperative Rydberg arrays that is both efficient and highly directional and may allow for terahertz-to-optical transduction. In the four-wave-mixing scheme, two lasers drive the system, coherently trapping the system in a dark ground-state manifold and coupling a signal transition, which may be in the terahertz, to an idler transition that may be in the optical regime. The photon-mediated dipole–dipole interaction between different emitters generates collective super- and subradiant dipolar surface modes, both on the signal and the idler transition. As the array is cooperative with respect to the signal transition, an incident signal photon can efficiently couple into the array and is admixed into dipolar idler modes by way of the drive. Under specific criticality conditions, this admixture is coupled into a superradiant idler mode, which primarily decays into a specific, highly directional optical photon that propagates within the array plane. Outside of the array, this photon may then be coupled into existing quantum devices for further processing. Using a scattering-operator formalism, we derive resonance and criticality conditions that govern this two-step process and obtain analytic transduction efficiencies. For lattices of infinite extension, we predict transduction efficiencies into specific spatial directions of up to 50%, while the overall, undirected transduction efficiency can be higher, beyond 90%. An analysis for finite arrays of $N^2$ emitters shows that the output is collimated into lobes that narrow as $1/\sqrt{N}$. Our scheme combines the broadband acceptance of free-space four-wave mixing with the efficiency, directionality, and tunability of cooperative metasurfaces, offering a route toward quantum coherent THz detection and processing for astronomical spectroscopy, quantum-networked sparse-aperture imaging, and other quantum-sensing applications.

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• Collective effects in atomic physics
• Collective effects in quantum optics
• Light-matter interaction
• Quantum optics
• Superradiance & subradiance
• Rotating wave approximation