Toward Spectral Engineering of Squeezed Light in High-Gain PDC

TL;DR

This work addresses how high-gain parametric down-conversion in dispersion-engineered waveguides shapes the spectral correlations of squeezed light. It develops a time-domain theory with a Bogoliubov input-output framework and Schmidt-mode analysis to extract a joint spectral amplitude and spectral purity $\\mathcal{P}$ under varying gain $G$ and phasematching. Key findings show that dispersion primarily governs the spectral purity evolution, with a distinct high-gain suppression of higher-order Schmidt modes when the pump group velocity lies between the signal and idler ($v_g^{(s)}<v_g^{(p)}<v_g^{(i)}$), notably for a dispersion angle around $\\theta \\approx 45^\\circ$. These insights offer practical, gain-tunable design rules for integrated squeezed-light sources, enabling rapid transition between multimode and near-single-mode operation without relying on pump bandwidth or phasematching form.

Abstract

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.

Figures (11)

• Figure 1: Schematic of PDC process in a waveguide where pump interacts with the nonlinear medium of the waveguide to generate signal and idler fields.
• Figure 2: Illustration of the three dispersion conditions under consideration, characterized by their respective angles ($\theta$) with respect to the frequency ($\omega_s$) axis. These dispersion conditions determine the phasematching characteristics of the system and thereby the shape and orientation of the joint spectral amplitude (JSA) at low gain Eq. (\ref{['eq:low_gain_jsa']}). Note that these schematics are not exact numerical JSAs but serve as a visual intuition to show the initial states that form the basis for our simulations.
• Figure 3: This figure presents the absolute value of the second moment of the two mode squeezed state [Eq. (\ref{['eq:spectral_corr_schmidt']})], which characterizes correlations between the signal and idler modes, for three dispersion conditions defined by the angles $\theta=0^\circ$, $45^\circ$, and $-11^\circ$. For each condition, two gain regimes are shown: low gain (peak powers $\mathrm{P}_p=68.54\,\mu\mathrm{W}$, and $\mathrm{P}_p=27.78\,\mu\mathrm{W}$) and high gain (peak powers $\mathrm{P}_p=1.37\,\mathrm{kW}$, and $\mathrm{P}_p=0.56\,\mathrm{kW}$). All panels are normalized to their respective maxima.
• Figure 4: This figure shows the relationship between spectral purity and gain for three dispersion conditions defined by angles $\theta = 0^\circ$, $45^\circ$, and $-11^\circ$, under both broadband and narrowband pump conditions. The inset highlights the crossing point of the spectral purity curves for the $\theta = 45^\circ$ and $\theta = 0^\circ$ conditions.
• Figure 5: In these figures, for a broadband pump in an unapodized WG (sinc-type phase matching), the mode contribution $p_{\ell}$ of the first three Schmidt modes is plotted versus gain for (a) $\theta=0^\circ$, (b) $\theta=45^\circ$, and (c) $\theta=-11^\circ$.