In long-haul optical continuous-wave frequency transfer via fiber, remote bidirectional Er$^+$-doped fiber amplifiers are commonly used to mitigate signal attenuation. We demonstrate for the first time the ultrastable transfer of an optical frequency
using a remote fiber Brillouin amplifier, placed in a server room along the link. Using it as the only means of remote amplification, on a 660 km loop of installed underground fiber we bridge distances of 250 km and 160 km between amplifications. Over several days of uninterrupted measurement we find an instability of the frequency transfer (Allan deviation of $Lambda$-weighted data with 1 s gate time) of around $1times10^{-19}$ and less for averaging times longer than 3000 s. The modified Allan deviation reaches $3times10^{-19}$ at an averaging time of 100 s, corresponding to the current noise floor at this averaging time. For averaging times longer than 1000 s the modified Allan deviation is in the $10^{-20}$ range. A conservative value of the overall accuracy is $1times10^{-19}$.
We demonstrate combined high-fidelity long-haul transfer of a linearly chirped, optical frequency and time transfer. In a proof-of-principle experiment we transfer an optical frequency with a linear chirp of around 238 kHz/s via a phase-stabilized un
derground fiber link of 150 km. We find a fractional frequency transfer instability (Allan deviation, 18000 s averaging time) and simultaneity of the chirped frequency between both ends on a level of around $2times10^{-19}$, where the active phase stabilization suppresses cumulative, symmetrical effects. In a second step, we demonstrate the remote measurement of synchronisation taking advantage of chirped-frequency transfer. The uncertainty of time transfer here is around 500 ps.
