Quantum nonlinear parametric interaction in realistic waveguides: a comprehensive study

TL;DR

This work develops a propagator-based framework that merges classical waveguide engineering with quantum nonlinear theory for $\chi^{(2)}$ processes to model realistic waveguide-based quantum light sources. It systematically analyzes fabrication-induced nonidealities—scattering losses, domain-writing errors, and geometry inhomogeneities—and quantifies their impact on heralded pure states, single-mode squeezing, broadband squeezed vacuum, and quantum frequency conversion. Key findings include a strong sensitivity to group-velocity dispersion, the disruptive role of waveguide geometry variations, and an upper bound on squeezing due to asymmetric GVM combined with pump self-phase modulation. The framework offers a path toward industrial-scale design of quantum light sources and motivates future work on non-Gaussian regimes, more complex photonic circuits, and dispersion-engineered material platforms.

Abstract

Nonlinear sources of quantum light are foundational to nearly all optical quantum technologies and are actively advancing toward real-world deployment. Achieving this goal requires fabrication capabilities to be scaled to industrial standards, necessitating precise modeling tools that can both guide device design within realistic fabrication constraints and enable accurate post-fabrication characterization. In this paper, we introduce a modeling framework that explicitly integrates the engineering tools used for designing classical properties of integrated waveguides with quantum mechanical theory describing the underlying nonlinear interactions. We analyze the validity and limitations of approximations relevant to this framework and apply it to comprehensively study how typical fabrication errors and deviations from nominal design -- common in practical waveguide manufacturing -- affect the nonlinear optical response. Our findings highlight, in particular, a critical sensitivity of the framework to group-velocity dispersion, the potentially disruptive role of geometric inhomogeneities in the waveguide, and an upper bound on single-mode squeezed-state generation arising from asymmetric group-velocity matching conditions.

Figures (8)

• Figure 1: a) Schematic depiction of a ridge waveguide affected by different effects associated with realistic waveguides. Dark regions represent areas where the material nonlinearity was inverted artificially. The coordinates $z_{l}$ correspond to the positions of the Trotter-Suzuki expansion described in Sec. III. b) Schematic depiction of the different processes considered for the quantitative analysis in Sec. IV and V, highlighting in- and outputs, the interacting wavelengths, group-velocity matching conditions, and the type of domain patterning.
• Figure 2: a) Effects of changes of different aspects of the waveguide geometry on the phase-mismatch of waveguides configured for single-mode/pure state generation (SM/PSG), broadband squeezed vacuum generation (BSVG), and QFC. We note, that, for every case, variations of the film thickness, a parameter rooted in the wafer fabrication, imparts the largest additional phase-mismatch. The dashed lines highlight the ideal, targeted waveguide geometry and the phase-mismatch that is compensated by the poling. b) Depiction of the parameter $\Delta \beta_{\text{\tiny TWM}} (z)$, used to capture the effects of waveguide inhomogeneities in our modeling framework (see Sec III). The data describing $\Delta \beta_{\text{\tiny TWM}} (z)$ is generated from a smoothed random walk with zero average and total range corresponding to the combination of geometry parameters in a) that give the maximal additional phase-mismatch. This range is quoted as 'maximal phase-mismatch' in Figs. \ref{['fig:PPGTable']}-\ref{['fig:QFCTable']}. The inset depicts reference values corresponding to the shaded areas in a), which, in our opinion, should be well attainable in practice. c) The poling pattern used to implement the gaussian phase-matching function used for single-mode/pure state generation and QFC. The pattern was calculated using AbranczykCustomPoling.
• Figure 3: Single-mode/pure state generation: JSAs in the left columns corresponds to markers highlighted in identical color in the parameter sweeps depicted in the right columns. Markers highlighted in light-blue and -green correspond to perfect waveguides with pump-pulses of 1.5e6 and 2.5e7 photons respectively. SN: Schmidt-number, PN: Number of down-converted photons, HSP: Squeezing parameter of the dominant Schmidt-mode, WG: Waveguide, DW: Domain writing.
• Figure 4: Broadband squeezed vacuum generation: JSAs in the left columns corresponds to markers highlighted in identical color in the parameter sweep depicted in the right column. Markers highlighted in light-blue correspond to perfect waveguides with pump-pulses of 5e3 photons. The curvature of the generated spectrum is a result of plotting in terms of wavelengths. SN: Schmidt-number, PN: Number of down-converted photons, HSP: Squeezing parameter of the dominant Schmidt-mode, WG: Waveguide, DW: Domain writing.
• Figure 5: Quantum frequency conversion: JSAs in the left columns corresponds to markers highlighted in identical color in the parameter sweep depicted in the right column. Markers highlighted in light-blue correspond to perfect waveguides with pump-pulses of 5e3 photons. CE: Conversion efficiency, S: Separability, WG: Waveguide, DW: Domain writing.