Strategies for generating separable photon triplets in waveguides and ring resonators

Photon triplet sources exhibit non-Gaussian features, a key property for applications in quantum computing and quantum information. However, spectral correlations can limit the performance and detection efficiency of these systems. Motivated by this observation, we present a theoretical analysis of the spectral properties of photon triplets generated through spontaneous third-order parametric down-conversion in photonic devices, and discuss strategies to quantify and minimize such correlations. We propose two approaches: dispersion engineering in waveguides and pump engineering in resonators. We apply these strategies in two realistic source designs, namely a high-index-contrast optical fiber and a silicon nitride microring resonator. Finally, we discuss detection strategies for probing non-Gaussian features of the triplet state. We find that it is feasible to achieve few-mode generation of photon triplets using state-of-the-art experimental systems, a crucial step toward practical applications of photon triplet sources in quantum technologies.