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arXiv:2601.23263

High-gain effects in broadband continuous-wave parametric down conversion sources and measurements with undetected photons

Martin Houde, Franz Roeder, Christine Silberhorn, Benjamin Brecht, Nicolás Quesada

quant-phphysics.opticsSubmitted Jan 30, 2026• Announced Feb 2, 2026• 0 citations
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Abstract

We study theoretically how high-gain effects affect the measurement outcome of visible signal spectra in undetected photon measurement schemes. We consider two interferometric configurations: firstly, the SU(1,1) interferometer where the idler incurs loss and additional dispersion in between two identical, lossless, squeezers; secondly, the induced coherence interferometer where the idler incurs loss and additional dispersion in between two identical, lossless, squeezers and where the second squeezer is seeded by the idler and a vacuum ancilla mode. Furthermore, we consider a distributed loss configuration where the idler incurs loss as it propagates in the nonlinear medium. Motivated by experimental evidence and due to the fact that broadband sources are ideal for these measurement schemes, we use the dispersive data of a third-order dispersion engineered integrated waveguide parametric down conversion (PDC) source presented in New Journal of Physics 26, 123025 (2024) to model the PDC spectra in the three configurations. For each configuration we consider the case of idler-only (i) absorption, (ii) additional dispersion, and (iii) the combined effects. We obtain results which outline the strength and weaknesses of the different configurations at different operation points.

Comments
19 pages, 16 figures, 3 appendices

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We study theoretically how high-gain effects affect the measurement outcome of visible signal spectra in undetected photon measurement schemes. We consider two interferometric configurations: firstly, the SU(1,1) interferometer where the idler incurs loss and additional dispersion in between two identical, lossless, squeezers; secondly, the induced coherence interferometer where the idler incurs loss and additional dispersion in between two identical, lossless, squeezers and where the second squeezer is seeded by the idler and a vacuum ancilla mode. Furthermore, we consider a distributed loss configuration where the idler incurs loss as it propagates in the nonlinear medium. Motivated by experimental evidence and due to the fact that broadband sources are ideal for these measurement schemes, we use the dispersive data of a third-order dispersion engineered integrated waveguide parametric down conversion (PDC) source presented in New Journal of Physics 26, 123025 (2024) to model the PDC spectra in the three configurations. For each configuration we consider the case of idler-only (i) absorption, (ii) additional dispersion, and (iii) the combined effects. We obtain results which outline the strength and weaknesses of the different configurations at different operation points.
Abstract We study theoretically how high-gain effects affect the measurement outcome of visible signal spectra in undetected photon measurement schemes. We consider two interferometric configurations: firstly, the SU(1,1) interferometer where the idler incurs loss and additional dispersion in between two identical, lossless, squeezers; secondly, the induced coherence interferometer where the idler incurs loss and additional dispersion in between two identical, lossless, squeezers and where the second squeezer is seeded by the idler and a vacuum ancilla mode. Furthermore, we consider a distributed loss configuration where the idler incurs loss as it propagates in the nonlinear medium. Motivated by experimental evidence and due to the fact that broadband sources are ideal for these measurement schemes, we use the dispersive data of a third-order dispersion engineered integrated waveguide parametric down conversion (PDC) source presented in Roeder et al (2024 New J. Phys. 26 123025) to model the PDC spectra in the three configurations. For each configuration we consider the case of idler-only (i) absorption, (ii) additional dispersion, and (iii) the combined effects. We obtain results which outline the strength and weaknesses of the different configurations at different operation points.
We theoretically compare the quantum Fisher information (QFI) for three configurations of absorption spectroscopy with undetected idler photons: an SU(1,1) interferometer with inter-source idler loss, an induced-coherence (IC) setup in which the idler partially seeds a second squeezer together with a vacuum ancilla, and a distributed-loss (DL) scheme with in-medium attenuation. We calculate the QFI as a function of parametric gain for both full and signal-only detection access. For losses below 99% and low to moderate gain, the SU(1,1) configuration provides the largest QFI. At high gain and intermediate loss, the IC scheme performs best, while under extreme attenuation (transmission <<< 1%) the DL model becomes optimal. These results delineate the measurement regimes in which each architecture is optimal in terms of information theory.
We investigated the spectral properties of squeezed light generated via parametric down-conversion in the high-gain regime, considering both unapodized and apodized dispersion-engineered waveguides. The gain-dependent evolution of these states is examined starting from the low-gain regime, which includes both highly correlated and nearly uncorrelated cases. For the unapodized configuration, we observe a monotonic increase in spectral purity with gain, whereas the apodized configuration exhibits a nonmonotonic dependence, initially decreasing and then recovering at higher gain. By combining Schmidt-mode analysis with a group-velocity-based interpretation, we explain why different dispersion conditions exhibit distinct gain-dependent behavior, specifically that rapid purification occurs when the pump group velocity lies between those of the signal and idler. Our study shows that the evolution of spectral purity is governed primarily by the underlying dispersion of the waveguide. These results demonstrate that dispersion engineering and parametric gain can be jointly exploited to tailor the spectral-mode structure of squeezed-light sources, enabling their optimization for a broad range of quantum applications.
Abstract We theoretically compare the quantum Fisher information (QFI) for three configurations of absorption spectroscopy with undetected idler photons: an SU(1,1) interferometer with inter-source idler loss, an induced-coherence (IC) setup in which the idler partially seeds a second squeezer together with a vacuum ancilla, and a distributed-loss (DL) scheme with in-medium attenuation. We calculate the QFI as a function of parametric gain for both full and signal-only detection access. For losses below 99% and low to moderate gain, the SU(1,1) configuration provides the largest QFI. At high gain and intermediate loss, the IC scheme performs best, while under extreme attenuation (transmission < 1%) the DL model becomes optimal. These results delineate the measurement regimes in which each architecture is optimal in terms of information theory.
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.