Time resolution at the quantum limit of two incoherent sources based on frequency resolved two-photon-interference

The Rayleigh criterion is a widely known limit in the resolution of incoherent sources with classical measurements in the spatial domain. Unsurprisingly the estimation of the time delay between two weak incoherent signals is afflicted by an analogue problem. In this work, we show the emergence of two-photon quantum beats in the frequency domain from the interference at a beam splitter of a photon emitted by a reference source and one from the two incoherent weak signals. We demonstrate, based on this phenomena, that with a relatively low number of measurements of the frequencies of the interfering photons either bunching or antibunching at the beam splitter output one can achieve a precision amounting to half of the quantum limit, independently of both the mode structure of the photonic wavepackets and the time delay to be estimated. The feasibility of the technique makes it applicable in astronomy, microscopy, remote clocks synchronization and radar ranging

💡 Research Summary

The paper addresses the fundamental problem of estimating the time delay Δt between two weak incoherent optical signals, a task that is classically limited by an analogue of the Rayleigh criterion when the delay is smaller than the temporal width of the optical field. The authors propose a quantum‑enhanced measurement scheme that exploits two‑photon interference in the frequency domain, rather than direct time‑resolved detection.

In the proposed setup, a reference photon, prepared in a known temporal mode, interferes at a balanced beam splitter with a probe photon that originates from either of the two incoherent sources. After the beam splitter, the two output ports are monitored by single‑photon cameras capable of resolving the photon frequencies ω and ω′. Each detection event yields a pair (Δω, X), where Δω = ω − ω′ is the frequency difference and X ∈ {B,A} indicates whether the photons bunched (both detected on the same camera, B) or anti‑bunched (detected on different cameras, A).

The authors derive the joint probability distribution

Pν(Δω,X;Δt) = ½ η C(Δω)