  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.
