Two-way optical frequency comparisons at 5*10^-21 relative stability over 100-km telecommunication network fibers

By using two-way frequency transfer, we implement a real-time frequency comparison over a uni-directional telecommunication network of 100 km using a pair of parallel fibers with simultaneous digital data transfer. The relative frequency stability is 10^-15 at 1s integration time and reaches 2*10^-17 at 40000s, three orders of magnitude below the one-way fiber instability. We also demonstrate ultrahigh-resolution comparison of optical frequencies with a bidirectional scheme using a single fiber. We show that the relative stability at 1s integration time is 7*10^-18 and scales down to 5*10^-21. The same level of performance is reached when an optical link is implemented with an active compensation of the fiber noise. The fractional uncertainty of the frequency comparisons was evaluated for the best case to 2*10^-20. These results open the way to accurate and high-resolution frequency comparison of optical clocks over intercontinental fiber networks.