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

TL;DR

This paper addresses how high-gain in broadband continuous-wave parametric down-conversion sources affects signal spectra in undetected-photon spectroscopy. It develops a dispersion-engineered, data-driven model to compare three sensing configurations—SU(1,1) interferometry, induced coherence, and distributed loss—and analyzes idler-only absorption and dispersion effects across gain regimes. The main findings show that increasing gain amplifies idler-loss signatures and shifts or distorts spectral oscillations in the SU(1,1) and IC setups, while distributed loss exhibits gain-dependent amplification and added-noise interactions; anomalous dispersion in the DL case yields gain-independent, mirror-like signatures that help differentiate from absorption. The results offer practical guidance for selecting source dispersion engineering and measurement strategies, including 2D interferograms and visibility analyses, to optimize broadband undetected-photon spectroscopy in regions where detectors are inefficient or unavailable.

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.

Figures (16)

• Figure 1: Schematic representation of the different sensing configurations and the respective loss implementations. (a) Interferometric sensing for SU(1,1) (solid orange lines) and IC (dotted orange line) models. Both nonlinear regions are taken to be identical and lossless. We treat losses via a beam splitter interaction (with transmission rate $\eta_{I}$ for the idler) between both nonlinear regions. To simulate optical path delays, we also allow the beam splitter interaction to induce additional dispersion for the idler mode ($\Phi_{I}$). SU(1,1) operation: both signal and idler seed the second nonlinear region. IC operation: only the idler seeds the second nonlinear region, newly generated ancilla mode is then combined with signal via a balanced beamsplitter. (b) DL model where the idler mode experiences decay rate ($\kappa_{I}$) as it propagates through the nonlinear region. Both losses and transmission rates are taken to be frequency dependent. P: pump; S: signal; I: idler; A: ancilla.
• Figure 2: Absorption feature in the measured signal spectrum around $845\,\mathrm{nm}$, which corresponds to an idler wavelength of $2900\,\mathrm{nm}$. The measured dip in the intensity can be attributed to an absorption of the idler field in the waveguide material throughout the generation process.
• Figure 3: Phase-matching argument (PMA) and signal intensity curves for vacuum inputs for both sets of parameters. (a) PMA for the flat parameters. (b) PMA for the skewed parameters. We see that the PMA plateau is no longer phase-matched. (c) Signal intensity curve for vacuum inputs for the flat parameters. (d) Signal intensity curve for vacuum inputs for the skewed parameters. Although the PMA plateau is not phase-matched, we still see some amplification. The red(green) lines in (a) and (b) correspond to the PMA values of the first zero of the signal intensity curves for low(high)-gain regime.
• Figure 4: Normalized intensity for the beamsplitter arm ($N^{\text{IC,BBS}}_{+}$) of the IC interferometer. Flat parameter set (a) without additional idler phases and (b) where additional idler phases cancel the linear contribution of $\Delta K(\omega)L/2$ (c.f. Sec. \ref{['sec:IC']}). Skewed parameter set (c) without additional idler phases and (d) where additional idler phases cancel the linear contribution of $\Delta K(\omega)L/2$. Green optimal curves represent the situation where the $\Delta K(\omega)L/2$ term is completely negated.
• Figure 5: Normalized signal intensity after an SU(1,1) inteferometer for the (a) flat and (b) skewed parameter sets in the low- and high-gain regimes. Near phase-matching in the flat parameter set gives rise to the second pass acting as a near-perfect squeezer and enhances the idler loss signature on the signal intensity. Lack of phase-matching in the skewed parameter set gives rise to gain-dependent operation of the second pass: in the low-gain regime, the second pass acts as an anti-squeezer in the plateau region.