Clock Synchronization with Weakly Correlated Photons

TL;DR

The paper demonstrates nano-second clock synchronization between crystal oscillators using weakly time-correlated, thermal-like light with a measured cross-correlation peak $g^{(2)}(0)=1.42$ and a coherence time of 180 ns. It implements a two-channel experimental setup with substantial symmetric loss, achieving 10 ns timing jitter over 25 hours and developing a Poisson-based peak-finding model that outperforms normal approximations under low-signal conditions. The work provides online peak tracking with exponential smoothing and active frequency compensation, and generalizes to other timing-correlated sources, with scalability considerations for multi-party star topologies and telecom-band implementations. This approach enables clock distribution without high-efficiency detectors or SPDC sources, paving the way for robust, long-distance quantum networks and practical distributed timing applications.

Abstract

Clock synchronization is necessary for communication and distributed computing tasks. Previous schemes based on photon timing correlations use pulsed light or photon pairs for their strong timing correlations. In this work, we demonstrate successful synchronization of crystal clocks using weakly time-correlated photons of 180 ns coherence time from a bunched light source. A synchronization timing jitter of 10 ns is achieved over symmetric -102 dB optical channel loss between two parties, over a span of 25 hours. We also present a model that gives better estimates to the coherence peak finding success probabilities under low signal.

Figures (5)

• Figure 1: (a) Simplified experimental setup for clock synchronization. Bunched light is sent to two different parties through separate -102 dB channels, before detection by Silicon avalanche photodetectors (Si APDs) and timestamping by time taggers referenced to independent crystal oscillators of frequencies $f_1$ and $f_2$. Singles count rate $s_1$ and $s_2$ of approximately 200 kcounts/s are recorded on each side. BS: beamsplitter; Att: attenuators. (b) Second-order coherence function $g^{(2)}(\tau)$ of the bunched light source, with the curve fit in black corresponding to $g^{(2)}(0)=1.42(1)$ peak and coherence time $\tau_c=180(6)$ ns. Error bars correspond to Poissonian errors from counting statistics. (c) Long-term frequency offset ($1 + \Delta{}u = f_1/f_2$), timing offset $\tau$, and event rates during a $25$ hour clock synchronization run between independent time taggers running on separate quartz crystal oscillators, after an initial frequency correction of $4.0$ ppm. Correlation peak tracking is performed using a $256$ ns coincidence window. The sharp spike and dip in event rates are attributed to laser mode hopping.
• Figure 2: A concurrent measurement of the actual frequency offset $\Delta u$ between the two external $10$ MHz clocks, as well as the corresponding error in the reconstructed frequency offset $\Delta u'$. The accuracy of the frequency served by the peak tracking algorithm is $3.2$ ppb on average.
• Figure 3: Success probabilities of finding the correct peak position, numerically obtained by performing $>\!\!10^7$ Monte Carlo trials for each $(N,\delta t)$ pair to estimate and interpolate the cumulative distribution in Eqn. \ref{['eqn:peakfinding']}. The parameters are singles detection rate $s_1=s_2=100$ kcounts/s, coincidence rate $c=650$ counts/s, bin overlap $\nu=0.5$, and frequency offset error of $\Delta{}u=50$ ppb (precompensation step size of 100 ppb), corresponding to the setup in Fig. \ref{['fig:result:main']} with an additional $3$ dB attenuation per channel.
• Figure 4: Characterization of peak tracking accuracy under a constant frequency offset $\Delta{}u=10$ ppb, with a time constant $\beta=50$ ms chosen for the exponential moving average filter used in the experiment. (a) Measurement of reported timing offsets (blue) against the actual offset (black) over a period of 30 seconds. The inset highlights a $\approx{}\!30$ ns timing error over a 0.5-second window, which suggests that a histogram fit does not improve accuracy. (b) Measurements of average offset error and jitter across different time constants $\beta$, over a measurement period of 10 minutes. Timing jitter is equivalent to the root-mean-squared error, and corresponds to 10 ns with $\beta=50$ ms (marked in gray dashed line). Peak tracking fails with time constants less than 5 ms.
• Figure 5: (a) Success probabilities of finding the correct peak position by solving Eqn. \ref{['eqn:peakfinding']}, given singles detection rate $s_1=s_2=100$ kcounts/s, coincidence rate $c=650$ counts/s, and bin overlap of $\nu=0.5$, and frequency offset error of $\Delta{}u=50$ ppb (precompensation step size of 100 ppb). (b) Corresponding probabilities using the normal approximation for observed accidental coincidences $X$ in Eqn. \ref{['eqn:peakfinding']}, with the same parameters. The probabilities are strongly dependent on $N$ and minimally with $\delta t$, similar to the estimations provided using the statistical significance framework.