Spectrally pure visible-telecom photon pairs via dispersion-engineered Si3N4 waveguides

We propose silicon nitride ($\mathrm{S}{\mathrm{i}}_{3}{\mathrm{N}}_{4}$) nanowaveguide-based CMOS-compatible integrated sources of spectrally pure visible-telecom photon pairs. Our designs are intrinsically devoid of spectral correlations, eradicating the need for narrow-band filtering that reduces the source brightness. Further, the signal photons lie in the visible--near-infrared (vis-NIR) band, which can provide increased heralding efficiency of the idler photon in the telecom band using high-efficiency single-photon detectors. For example, a rectangular-cross-section silica-clad $\mathrm{S}{\mathrm{i}}_{3}{\mathrm{N}}_{4}$ nanowaveguide with dimensions $680\text{~nm}\ifmmode\times\else\texttimes\fi{}840\text{~nm}$ and length 7 cm provides a heralded single-photon purity of approximately $91\mathrm{%}$ for a pump wavelength of 956.8 nm and a pump bandwidth of 1200 GHz, with the signal and idler lying in the visible and telecom bands at approximately $701$ nm and approximately $1505$ nm, respectively, demonstrating a peak spectral brightness of approximately $1.2\ifmmode\times\else\texttimes\fi{}{10}^{4}$ photon $\mathrm{pairs}/\mathrm{s}/\mathrm{nm}/{\mathrm{mW}}^{2}$ for a linear propagation loss of 0.5 dB/cm. The effect of propagation losses on the purity is also studied for such source designs. We also propose some designs capable of generating high-purity photon pairs to address various specific vis-NIR quantum memory transitions with telecom-band interfacing for long-distance hybrid quantum networks. Such compact on-chip sources could have potential applications in various quantum technologies, such as sensing, simulation, computing, communication, and networking.