Quantum frequency conversion (QFC) between the visible and telecom is a key functionality to connect quantum memories over long distances in fiber-based quantum networks. Current QFC methods for linking such widely-separated frequencies, such as sum/difference frequency generation and four-wave mixing Bragg scattering, are prone to broadband noise from the pump laser(s). To address this issue, we propose to use third-order sum/difference frequency generation (TSFG/TDFG) for an upconversion/downconversion QFC interface. In this process, two pump photons combine their energy and momentum to mediate frequency conversion across visible and telecom bands, bridging a large spectral gap with long-wavelength pump pho-tons, which is particularly beneficial from the noise perspective. We show that waveguide-coupled silicon nitride microring resonators can be designed for efficient QFC between 606 nm and 1550 nm via a 1990 nm pump through TSFG/TDFG. We simulate the device dispersion and coupling, and from the simulated parameters estimate that the frequency conversion can be efficient (>80 %) at 50 mW pump power. Our results suggest that microresonator-based TSFG/TDFG is promising for compact, scalable, and low power QFC across large spectral gaps.
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