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Optica Quantum

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

A. Gatti, Matteo Clerici, Lucia Caspani

Published May 13, 2025• 8 citations
Publisher

Abstract

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.

DOI
10.1364/opticaq.554539

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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.
Long ago, it was predicted that stimulating two-photon processes such as two-photon absorption (TPA) and second harmonic generation (SHG) with entangled photons produced by parametric down-conversion (PDC) could result in higher efficiencies compared to classical illumination [1]. This was experimentally demonstrated for SHG [2] and TPA [3], where, however, the classical comparison was performed by adding losses to the PDC state rather than employing a true classical reference. In addition, these results considered spatially single-mode PDC radiation and were conducted at low photon fluxes, where the PDC modes are, on average, populated by less than one photon. This resulted in an extremely low SHG/TPA signal, considered of limited practical use for metrological applications (such as two-photon fluorescence microscopy or SHG imaging - see, e.g., [4]). A recent theoretical investigation [5] highlighted that a proper analysis of quantum-enhanced two-photon processes requires a fully spatiotemporal model of the nonlinear interactions. It further showed that highly multimode (in space and time) entangled PDC photons can provide a quantum advantage compared to an equivalent classical pulse, even in regimes well beyond the “one-photon-per-mode” limit, considered the boundary of quantum behavior.
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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.
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Integrated nonlinear optical devices for the generation of twin photon beams are expected to be a key element for the development of quantum information techniques. This paper presents a quantum theory analysis of counterpropagating twin photon generation (CPTPG) by spontaneous parametric downconversion. Full descriptions of the quantum states of the twin photon beams having unique features are obtained in the Heisenberg and Schrödinger pictures. Mathematical expressions useful for device design and quantitative prediction of the performances, such as efficiency, wavelength spectrum and bandwidth, and photon correlation time, are deduced. Numerical data are given for specific quasi-phase-matchedLiNbO3{\rm LiNbO}_{\bf 3}LiNbO3​waveguide CPTPG devices.