High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link

To significantly improve the frequency references used in radio-astronomy and the precision measurements in atomic physics, we provide frequency dissemination through a 642-km coherent optical fiber link. On the frequency transfer, we obtained a frequency instability of 3x10^- 19 at 1,000 s in terms of Allan deviation on a 5-mHz measurement bandwidth, and an accuracy of 5x10^-19. The ultimate link performance has been evaluated by doubling the link to 1,284 km, demonstrating a new characterization technique based on the double round trip on a single fiber. This method is an alternative to previously demonstrated techniques for link characterization. In particular, the use of a single fiber may be beneficial to long hauls realizations in view of a continental fiber network for frequency and time metrology, as it avoids the doubling of the amplifiers, with a subsequent reduction in costs and maintenance. A detailed analysis of the results is presented, regarding the phase noise, the cycle-slips detection and removal and the instability evaluation. The observed noise power spectrum is seldom found in the literature; hence, the expression of the Allan deviation is theoretically derived and the results confirm the expectations