Optical frequency transfer over a single-span 1840-km fiber link

We demonstrate optical frequency transfer over an 1840 km underground optical fiber link using a single-span stabilization. To compensate for more than 420 dB of optical attenuation of the light we use twenty Erbium doped fiber amplifiers along the entire link and two additional fiber Brillouin amplifiers. The good passive stability of our fiber link allows us to reach short term instabilities expressed as the modified Allan deviation of 3 × 10^-15 for a gate time τ of 1 s reaching 4 × 10^-19 in just 100 s. By comparing the sent and transferred frequencies we find no systematic offset within the statistical uncertainty of about 3 × 10^-19. The spectral noise distribution of our fiber link at low Fourier frequencies leads to a τ^-2 slope in the modified Allan deviation.