By projecting onto complex optical mode profiles, it is possible to estimate arbitrarily small separations between objects with quantum-limited precision, free of uncertainty arising from overlapping intensity profiles. Here we extend these techniques to the time-frequency domain using mode-selective sum-frequency generation with shaped ultrafast pulses. We experimentally resolve temporal and spectral separations between incoherent mixtures of single-photon level signals ten times smaller than their optical bandwidths with a ten-fold improvement in precision over the intensity-only Cram\'er-Rao bound.
@article{arxiv.1805.02491,
title = {Quantum-limited time-frequency estimation through mode-selective photon measurement},
author = {John M. Donohue and Vahid Ansari and Jaroslav Řeháček and Zdeněk Hradil and Bohumil Stoklasa and Martin Paúr and Luis L. Sánchez-Soto and Christine Silberhorn},
journal= {arXiv preprint arXiv:1805.02491},
year = {2018}
}