Filming chemical reactions or atoms in motion is one of the greatestscientific dreams yet to be accomplished which requires sub-atomicspatiotemporal resolution. Newly emerging X-ray free electron lasers andlaser-based attoscience centers are the most likely candidates to succeed firstthanks to their angstrom-level radiation. To provide the necessary temporalresolution, these facilities must be able to synchronize numerous mode-lockedlasers with ultra-high precision across kilometer-distances. Here, we report asynchronous mode-locked laser network incorporating two remote slave lasers atdifferent central wavelengths and repetition rates over 4.7-km distance. Thenetwork exhibits a record-low timing drift of 0.6 fs RMS below 1 Hz over 40 hreaching the 20$^{th}$ decimal uncertainty in ~8000-s averaging time.Short-term stability measurements show an out-of-loop timing jitter of only 1.3fs RMS integrated from 1 Hz to 1 MHz. We also present a comprehensive noiseanalysis of the network considering both quantum noise and technical noisesources. For the first time in literature, we reveal the standard quantum limitfor the timing jitter acquired by optical pulses when traveling in fiber links.Our comprehensive feedback loop analysis reveals nine technical noise sourcesout of which the slave lasers inherent jitter dominates with 1.26 fs RMS. Thissuggests that timing precision of the network is not limited by oursynchronization scheme and could be improved even further by developing lowernoise mode-locked lasers.
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