Quantum-limited optical delay sensing across an enhanced dynamic range by frequency-resolving two-photon interference

Optical sensing schemes that rely on two-photon interference provide a powerful platform for precision metrology, although they are inherently constrained by a trade-off between dynamic range and measurement precision. To overcome this limitation, we sample the frequencies of two interfering photons, which extends the sensitivity in the time domain. This enhances the dynamic range of optical delay estimation by up to twenty times compared to the non-resolved estimates. We demonstrate this approach with independent photon sources and show the behaviour of finite frequency resolving detectors. This technique enables scan-free nanometre resolution depth sensing over a millimetre-scale range, with applications in biological and nanomaterial imaging.