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arXiv:2610.06194

A robust framework for the comprehensive characterisation of parametric down-conversion sources

Denis A. Kopylov, Michael Stefszky, Christine Silberhorn

quant-phphysics.opticsSubmitted Oct 5, 2026• Announced Oct 6, 2026• 0 citations
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Abstract

Reliable verification of squeezed-light sources is essential for photonic quantum technologies. High-dimensional quantum optical networks demand single-mode, pure squeezed states which, in principle, can be generated through careful engineering of parametric down-conversion-based (PDC) sources. However, due to the imperfections of optical components, the generated state is never pure and commonly contains internal mode structure. Existing characterisation techniques, based on either joint spectral intensity or normalized second-order correlation functions, work under the assumption that the probed state is pure, and therefore can result in incomplete or misleading assessment of the source quality. Here, we develop a device-agnostic characterisation framework for PDC-based sources with distinguishable signal and idler fields. Treating the source as a black box producing a mixed multimode Gaussian state, we find a lower bound for the state purity, which can be experimentally determined via mode-unresolved measurements. Our approach enables a holistic assessment of realistic squeezed-light source quality without requiring a detailed model of the nonlinear device and its surrounding optical network, providing practical benchmarks for optimizing sources for state-of-the-art quantum applications.

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Parametric down-conversion (PDC) forms one of the basic building blocks for quantum optical experiments. However, the intrinsic multimode spectral-temporal structure of pulsed PDC often poses a severe hindrance for the direct implementation of the heralding of pure single photon states or, for example, continuous-variable entanglement distillation experiments. To get rid of multimode effects narrowband frequency filtering is frequently applied to achieve a single-mode behaviour. To date, the theoretical models of filtered PDC, however, only account for filtering in the low gain regime, where only a few photon-pairs are emitted at any single point in time. In this paper we extend these theoretical descriptions and present a rigorous theoretical model for filtered type-II PDC. Our theoretical investigations reveal that filtering a multimode type-II PDC state, followed by a careful optimization of the measurement basis, effectively achieves a single-mode behaviour and further enables the generation of single-mode EPR-entanglement. Considering the ever increasing brightness of PDC sources our developed theoretical framework, enables the accurate description of filtered PDC in quantum optical experiments.

•Mar 12, 2014•1 citation
Reliable verification of squeezed-light sources is essential for photonic quantum technologies. High-dimensional quantum optical networks demand single-mode, pure squeezed states which, in principle, can be generated through careful engineering of parametric down-conversion-based (PDC) sources. However, due to the imperfections of optical components, the generated state is never pure and commonly contains internal mode structure. Existing characterisation techniques, based on either joint spectral intensity or normalized second-order correlation functions, work under the assumption that the probed state is pure, and therefore can result in incomplete or misleading assessment of the source quality. Here, we develop a device-agnostic characterisation framework for PDC-based sources with distinguishable signal and idler fields. Treating the source as a black box producing a mixed multimode Gaussian state, we find a lower bound for the state purity, which can be experimentally determined via mode-unresolved measurements. Our approach enables a holistic assessment of realistic squeezed-light source quality without requiring a detailed model of the nonlinear device and its surrounding optical network, providing practical benchmarks for optimizing sources for state-of-the-art quantum applications.
Summary form only given. Recent advances in the design of broadband parametric down-conversion (PDC) sources have opened the possibility to attain a regime of high squeezing previously unacessible in the pulsed domain [1]. However, characterising a PDC source is a challenging task when multiple spectral modes are being squeezed simultaneously and one wants to determine the number of squeezers and their relative strengths. Moreover, as one approaches the high squeezing regime, a number of nonlinear effects that are not usually considered when the source is operated at low pump power become relevant [2, 3].Here we present a technique to perform a complete and self-referenced characterisation of a broadband PDC source using only classical measurements. Often, PDC sources are described by their joint spectral amplitude, which conveys the frequency correlations between the generated photons. Our method complements the information contained in the joint spectrum with a measurement of a second-order process that to our knowledge has not been directly measured until now. Generally, a PDC process can be described as a Bogoliuvov transformation of the bosonic operators of the formaouts (ω) = f dω'Us,s(ω,ω') ains + f dω''Us,i(ω,ω'')(ain i (ω''))† for the signal and analogously for the idler mode. In our work we show that these transfer functions, Us,s(i,i) and Us,i(i,s), can be measured in the stimulated regime [4,5], by scanning the wavelength of a narrowband seed laser and performing a frequency resolved intensity measurement of the generated light.
Parametric down-conversion (PDC) is the established standard for the practical generation of a multiplicity of quantum optical states. These include two-mode squeezed vacuum, heralded non-Gaussian states and entangled photon pairs. Detailed theoretical studies provide insight into the time-frequency (TF) structure of PDC, which are governed by the complex-valued joint spectral amplitude (JSA) function. However in experiments, the TF structure of PDC is mostly characterised by intensity measurementsthat forbid access to the important phase of the JSA. In this paper, we present an amplitude-sensitive quantum process tomography technique that combines methods from ultrafast optics and classical three-wave mixing. Our approach facilitates a direct and phase-sensitive time-frequency tomography of PDC with high spectral resolution and excellent signal-to-noise ratio. This is important for all quantum optical applications, which rely on engineered parametric processes and base on minute knowledge of the quantum wave-function for the generation of tailored photonic quantum states.
Low-photon-number sources can exhibit non-classical, counterintuitive behavior that can be exploited in the developing field of quantum technology. Single photons play a special role in this arena since they represent the ultimate lowphoton- number source. They are considered an important element in various applications such as quantum key distribution, optical quantum information processing, quantum computing, intensity measurement standards, and others yet to be discovered in this developing field. True deterministic sources of single photons on demand are currently an area of intensive research, but have not been demonstrated in a practical setting. As a result, researchers commonly default to the well-established workhorse: spontaneous parametric down-conversion generating entangled signal-idler pairs. Since this source is thermal-statistical in nature, it is common to use a detected idler photon to herald the production of a signal photon. The need exists to determine the quality of the single photons generated in the heralded signal beam. Quite often, the literature reports a "heralded second-order coherence function" of the signal photons conditioned on the idler photons using readily available single-photon detectors. In this work, we examine the applicability of this technique to single-photon characterization and the consequences of the fact that the most commonly used single-photon detectors are not photon-number resolving. Our results show that this method using non-photonresolving detectors can only be used to characterize the signal-idler correlations rather than the nature of the signalphoton state alone.
Squeezed light has evolved into a powerful tool for quantum technology, ranging from quantum-enhanced sensing and quantum-state engineering based on partial postselection techniques.The pulsed generation of squeezed light is of particular interest, as it can provide accurate time stamps and a physically defined temporal mode, which are highly preferred in complex communication networks and large-scale information processing.However, the multimode feature of pulsed squeezing limits the purity of the output state, negatively impacting its application in quantum technology.Previous demonstrations and analysis of pulsed squeezing focus on single-pass configurations and synchronously pumped free-space cavities.In this paper, we propose a different approach to generate pulsed squeezing with high temporal purity, where a parametric down-conversion process in integrated photonic cavities is pumped by a single-pass pulse.We show that the effective mode number of the output pulsed squeezing approaches unity.Such a high-purity squeezed light can be realized with broad parameters and a low pump power, providing a robust approach to generating large-scale quantum resources.
We implement an ultrafast pulsed type-II parametric down conversion source in a periodically poled KTP waveguide at telecommunication wavelengths with almost identical properties between signal and idler. As such, our source resembles closely a pure, genuine single mode photon pair source with indistinguishable modes. We measure the joint spectral intensity distribution and second order correlation functions of the marginal beams and find with both methods very low effective mode numbers corresponding to a Schmidt number below 1.16. We further demonstrate the indistinguishability as well as the purity of signal and idler photons by Hong-Ou-Mandel interferences between signal and idler and between signal/idler and a coherent field, respectively. Without using narrowband spectral filtering, we achieve a visibility for the interference between signal and idler of 94.8% and determine a purity of more than 80% for the heralded single photon states. Moreover, we measure raw heralding efficiencies of 20.5% and 15.5% for the signal and idler beams corresponding to detector-loss corrected values of 80% and 70%. (C) 2013 Optical Society of America
Parametric down-conversion (PDC) forms one of the basic building blocks for quantum optical experiments. However, the intrinsic multimode spectral-temporal structure of pulsed PDC often poses a severe hindrance for the direct implementation of the heralding of pure single photon states or, for example, continuous-variable entanglement distillation experiments. To get rid of multimode effects narrowband frequency filtering is frequently applied to achieve a single-mode behaviour. To date, the theoretical models of filtered PDC, however, only account for filtering in the low gain regime, where only a few photon-pairs are emitted at any single point in time. In this paper we extend these theoretical descriptions and present a rigorous theoretical model for filtered type-II PDC. Our theoretical investigations reveal that filtering a multimode type-II PDC state, followed by a careful optimization of the measurement basis, effectively achieves a single-mode behaviour and further enables the generation of single-mode EPR-entanglement. Considering the ever increasing brightness of PDC sources our developed theoretical framework, enables the accurate description of filtered PDC in quantum optical experiments.