Free-space dissemination of time and frequency with 10^-19 instability over 113 km

Networks of optical clocks find applications in precise navigation^1,2, in efforts to redefine the fundamental unit of the 'second'^3-6 and in gravitational tests⁷. As the frequency instability for state-of-the-art optical clocks has reached the 10^-19 level^8,9, the vision of a global-scale optical network that achieves comparable performances requires the dissemination of time and frequency over a long-distance free-space link with a similar instability of 10^-19. However, previous attempts at free-space dissemination of time and frequency at high precision did not extend beyond dozens of kilometres^10,11. Here we report time-frequency dissemination with an offset of 6.3 × 10^-20 ± 3.4 × 10^-19 and an instability of less than 4 × 10^-19 at 10,000 s through a free-space link of 113 km. Key technologies essential to this achievement include the deployment of high-power frequency combs, high-stability and high-efficiency optical transceiver systems and efficient linear optical sampling. We observe that the stability we have reached is retained for channel losses up to 89 dB. The technique we report can not only be directly used in ground-based applications, but could also lay the groundwork for future satellite time-frequency dissemination.