Enhancing upconversion with space-time entanglement: from twin photons to twin-beams

We investigate the use of entangled photons generated by parametric downconversion to improve the efficiency of second harmonic generation (SHG). Using a fully three-dimensional model for the nonlinear interactions, we obtain quantitative predictions of the efficiency of quantum-enhanced SHG and identify the critical parameters to optimize the process. By a careful control of the spatial and temporal degrees of freedom, we demonstrate a robust quantum advantage, extending to illumination fluxes well above the limits traditionally considered in the literature. Our analysis offers valuable insights into the ongoing debate on quantum-enhanced two-photon processes and helps establish their usefulness in applications.