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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

QuaNtum-Enhanced Second Harmonic Generation beyond the Photon Pairs Regime

T. Dickinson, Ivi Afxenti, Giedre Astrauskaite, L. Hirsch, Samuel Nerenberg, O. Jedrkiewicz, Daniele Faccio, Marie Caroline Müllenbroich, A. Gatti, Matteo Clerici, Lucia Caspani

Published Jun 23, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1109/cleo/europe-eqec65582.2025.11110849

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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.
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.
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.
The harnessing of the nonclassical properties in photon pairs generated by the process of Spontaneous Parametric Down Conversion (SPDC) to enhance two-photon interactions has long intrigued researchers. Their use in light-matter interactions has been proven to improve efficiency either by increasing the rate of generation or by suppressing noise. Namely, the processes of Entangled Sum Frequency Generation (eSFG) and Entangled Two Photon Absorption (eTPA) have been shown to produce more photons when stimulated with entangled photons than the classical versions of the effects. This has only been effective so far at very low intensities, which, alongside the inability to reproduce previous experimental results, has caused debates about the usefulness of the effect. In the presented work, I aim to shed light on the topic by employing a carefully crafted source of entangled photon pairs to improve two-photon effects. I attempt to demonstrate, through a series of experiments, that the quantum enhancement can be observed at an order of magnitude higher than previously thought possible. To solidify the results, a direct comparison of the quantum effect was conducted by investigating the performance of the phenomenon when it is stimulated by classical radiation from a laser. Our results confirm a quantum improvement in a regime previously considered impossible, and they enabled us to examine the ramifications of the effect on imaging. By doing so, we consider real-life microscopy applications, and therefore, we can set limits to the effect.