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

TL;DR

This paper introduces a quantum sensing method that uses time sampling of quantum beats to estimate the frequency difference between two photons with ultimate precision, surpassing standard measurement limits.

Contribution

It proposes a novel time-resolved measurement protocol for frequency estimation that reaches quantum-limited precision without requiring entanglement.

Findings

Achieves quantum-limited precision in frequency difference estimation.

Saturates the Cramér-Rao bound with around 1000 measurements.

Overcomes limitations of traditional frequency-resolving detectors.

Abstract

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, the frequency shift between two photons can be estimated with the ultimate precision achievable in nature, 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 $\sim 1000$ sampling measurements, the Cram\'{e}r-Rao bound is saturated independently of the value of the difference in frequency.