E-21 Level Instability Frequency Dissemination over 2067 km noisy Telecommunication Infrastructure

Abstract: The realization of ultra stable optical frequency transmission through fiber networks is critical for advancing global optical frequency standards and enabling applications such as redefining the second in the International System of Units, geophysical sensing, quantum network construction, and fundamental physics experiments. However, achieving high reliability and low instability optical frequency carrier transmission links over distances exceeding thousands of kilometers remains technically challenging, thereby limiting the scalability and reliability of such networks. In this study, we experimentally demonstrate that the noise accumulation in long distance optical links can be mitigated by narrowband purification of the optical signal's phase noise, enabling optical links of theoretically unlimited length. Additionally, we implemented digital optical phase measurement and feedback technology to calibrate noise compensation deviations caused by inconsistencies in round trip optical frequencies, enhancing link stability. By adopting digital phase measurement instead of traditional phase detectors, we expanded the dynamic noise tolerance range of the optical phase-locked loop, significantly improving system reliability. Ultimately, on a 2067 km telecommunications fiber link with a noise level exceeding 5000 rad^2/Hz.km, we achieved an optical frequency transfer with a daily instability of 2.9 E-21 without experiencing any optical cycle slips maintaining continuous operation for four days. This work establishes a technical foundation for leveraging existing fiber resources to construct global scale optical frequency standard networks.