Asynchronous Multi-photon Interference for Quantum Networks

TL;DR

This work develops and experimentally validate a theoretical framework that quantitatively describes time-resolved multi-photon interference in the CW regime that explicitly incorporate detector timing jitter, photon coherence time, and temporal post-selection and determines the coincidence window that maximizes usable four-photon rates for a target visibility.

Abstract

Advanced quantum communication protocols require high-visibility quantum interference between photons generated at distant nodes, which places stringent demands on optical synchronization. Conventionally, synchronization of optical wave packets relies on pulsed sources and precise optical path stabilization. An alternative approach employs continuous-wave (CW) photon-pair sources, where temporal indistinguishability is enforced by post-selecting detection events within a coincidence window $τ_w$ shorter than the photon coherence time $T_c$. Despite its conceptual simplicity, the quantitative relation between relevant time scales, achievable interference visibility, and usable multi-photon rates has remained unclear. Here, we develop in detail and experimentally validate a theoretical framework that quantitatively describes time-resolved multi-photon interference in the CW regime. We explicitly incorporate detector timing jitter, photon coherence time, and temporal post-selection. The model is verified using four-photon Hong-Ou-Mandel interference measurements. Based on this validated framework, we determine the coincidence window that maximizes usable four-photon rates for a target visibility. Finally, we compare CW and pulsed SPDC sources under equivalent indistinguishability constraints and show that CW operation can achieve comparable rates while relaxing optical synchronization requirements.

Figures (13)

• Figure 1: (a) Realization of temporal indistinguishability in entanglement swapping via time-synchronized pulsed photon sources. (b) Entanglement swapping with continuous-pumped photon pair sources. Temporally indistinguishable photons can be post-selected with single photon detectors if the coherence time of photons $T_c$ exceeds the coincidence window $\tau_w$ of detection events. (c) Detection of two photon wave packets with given coincidence window $\tau_w$. Since the coincidence window is larger than the coherence time $T_c$, photon pairs with large temporal distances can be inaccurately counted as a simultaneous coincidence. (d) Continuous emission of photon pairs from two CW sources, where among all pairs, the temporally indistinguishable photons (green) can be post-selected.
• Figure 2: (a) We assume the outer photons are detected first. The coincidence window $\tau_{1,4}$ sets the maximum allowed time difference between the detection events in the spatial modes $1$ and $4$, if $j<\tau_{1,4}$ is ensured. Because of the strong time correlation within each pair, this $\tau_{1,4}$ window predetermines the temporal separation—and thus the indistinguishability-of the photons in modes $2$ and $3$. The coincidence windows $\tau_{2,3}$ in spatial modes $2^{\prime}$ and $3^{\prime}$ does not affect this indistinguishability; it determines the probability of successfully capturing the wave packets of these photons. (b) The illustration of the coincidence windows relative to the trigger photon in the spatial mode $1$. This example illustrates that the photons exit into the same spatial mode $3^{\prime}$, leaving $2^{\prime}$ empty. A noise photon (dashed wave packet) can then occupy $2^{\prime}$ and produce a false fourfold. The dashed window in mode 4 indicates the $\tau$-dependent shift of the $\tau_{1,4}$ coincidence window. PD: photon detector; PS: photon-pair source.
• Figure 3: Experimental setup for performing four-photon HOM interference. A CW telecom laser is up-converted and then split into two paths to pump two SPDC sources, A and B (blue boxes). The generated two-photon states are separated with a wavelength division multiplexer (WDM) according to their higher or lower frequencies, followed by tight filtering with a fiber Bragg grating, as described in the left inset. The signal photons (blue) are used to herald the interference, while the idler photons (red) are interfered at a polarization-maintaining fiber beam splitter (FBS). CIRC: circulator; PBS: polarization beam splitter; PC: polarization controller; ppLN: periodically-poled lithium niobate waveguide.
• Figure 4: (a) Normalized reflection spectrum of the FBG filter with a bandwidth of $\Delta\lambda=41$ pm. The wavelength-dependent reflectance was determined by normalizing the reflected signal to the incident probe spectrum. (b) Two-photon coincidence counts for the source B (dots) compared with the calculated and normalized coherence function without (dashed purple curve) and with the phase model (solid red curve).
• Figure 5: Time-resolved HOM dip for different coincidence windows $\tau_{1,4}$ of the outer photons, where the coincidence window of the photons in modes $2^{\prime}$ and $3^{\prime}$ is set to $\tau_{2,3}= 2000$ ps. For the theoretical calculation, we normalized Eq. \ref{['HOMmain']} according to experimental photon count rate for $\tau_{1,4}= 40$ ps. The same normalization is used for the rest of the theoretical prediction. The total rate was measured over a $1.5$-hour period.