Quantum-enhanced second harmonic generation beyond the photon pairs regime

Two-photon processes are crucial in applications like microscopy and microfabrication, but their low cross section requires intense illumination and limits, e.g., the penetration depth in nonlinear microscopy. Entangled states have been proposed to enhance the efficiency of two-photon interactions and have shown effectiveness at low intensities. This quantum enhancement is generally believed to be lost at high intensities, for more than one photon per mode, raising doubts about its usefulness. We explored experimentally and theoretically two-photon processes driven by entangled photons at intensities beyond this threshold and compared the results with the classical case. We found that a quantum advantage can still be observed at nearly one order of magnitude higher intensities than previously assumed. Our findings show a potential path for exploiting quantum-enhanced two-photon processes in practical applications.