Brillouin amplification supports1×10−20uncertainty in optical frequency transfer over 1400 km of underground fiber

Abstract

We investigate optical frequency transfer over a 1400 km loop of underground fiber connecting Braunschweig and Strasbourg. Largely autonomous fiber Brillouin amplifiers are the only means of intermediate amplification used here. This allows phase-continuous measurements over periods up to several days. Over a measurement period of about three weeks we find a weighted mean of the transferred frequency's fractional offset of $(1.1\pm 0.4)\times {10}^{-20}$. In the best case we find an instability of $6.9\times {10}^{-21}$ and a fractional frequency offset of $4.4\times {10}^{-21}$ at an averaging time of around 30 000 s. These results represent an upper limit for the uncertainty over 1400 km when using a chain of remote Brillouin amplifiers, and allow one to compare the world's best optical clocks.