  Hong-Ou-Mandel interferometry takes advantage of the quantum nature of
two-photon interference to increase the resolution of precision measurements of
time-delays. Relying on few-photon probe states, this approach is applicable
also in cases of extremely sensible samples and it achieves attosecond
(nanometer path length) scale resolution, which is relevant to cell biology and
two-dimensional materials. Here, we theoretically analyze how the precision of
Hong-Ou-Mandel interferometers can be significantly improved by engineering the
spectral distribution of two-photon probe states. In particular, we assess the
metrological power of different classes of biphoton states with non-Gaussian
time-frequency spectral distributions, considering the estimation of both time-
and frequency-shifts. We find that grid states, characterized by a periodic
structure of peaks in the chronocyclic Wigner function, can outperform standard
biphoton states in sensing applications. The considered states can be feasibly
produced with atomic photon sources, bulk non-linear crystals and integrated
photonic waveguide devices.
