High-Precision Measurement of Time Delay with Frequency-Resolved Hong-Ou-Mandel Interference of Weak Coherent States

We demonstrate a scheme for high-precision measurements of time delay based on frequency-resolved Hong-Ou-Mandel (HOM) interference. Our approach is applied to weak coherent states and exploits an array of single-photon avalanche diodes (SPADs). Unlike conventional HOM experiments, our setup enables high-precision measurements producing an uncertainty per coincidence of about $\sim 10$ ps even for photons separated by delays up to $\sim 4$ ps so much greater than their coherence time where ordinary non-resolved HOM fails. This result confirms our newly developed theoretical predictions that consider, differently from previous theoretical results, a finite frequency resolution in the detection. We compare the performance of this scheme against the conventional non-resolved case. Experimental data align well with the predictions of quantum estimation theory, demonstrating a significant reduction in the uncertainty. Due to the physics of the frequency-resolved HOM effect, the gain in precision is particularly high when the estimated time delay is much longer than the coherence time.

💡 Research Summary

The paper presents a novel scheme for high‑precision time‑delay estimation that leverages frequency‑resolved Hong‑Ou‑Mandel (HOM) interference of weak coherent states. Traditional HOM interferometry, which relies on bucket detectors that ignore frequency information, loses sensitivity once the delay Δt exceeds the photon coherence time τ (Δt/τ > 1). In that regime the two photons become temporally distinguishable and the characteristic HOM dip disappears, limiting the achievable precision.

The authors theoretically model two identical photons with a Gaussian spectral distribution f(ω) of variance σ² = 1/(4τ²). After a balanced beam splitter, the joint detection probability for frequencies ω₁ and ω₂ is
P_A/B(ω₁,ω₂) = ½ f(ω₁)f(ω₂)