Quantum-limited estimation of the frequency shift between two interfering photons by time sampling of their quantum beats

We present a sensing scheme for estimating the frequency difference of two non-entangled photons. The technique consists of time-resolving sampling measurements at the output of a beam splitter. With this protocol, we can achieve the ultimate precision for the estimation of the frequency shift between two non-entangled photons, overcoming the limits in precision and the range of detection of frequency-resolving detectors employed in standard direct measurements of the frequencies. The sensitivity can be increased by increasing the coherence time of the photons. We show that, already with ∼ 1000 sampling measurements, the Cramér–Rao bound for the specific input state chosen is saturated independently of the value of the difference in frequency.