Comparing Optical Oscillators across the Air to Milliradians in Phase and 10−17 in Frequency

We demonstrate carrier-phase optical two-way time-frequency transfer (carrier-phase OTWTFT) through the two-way exchange of frequency comb pulses. Carrier-phase OTWTFT achieves frequency comparisons with a residual instability of $1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ at 1 s across a turbulent 4-km free space link, surpassing previous OTWTFT by 10--20 times and enabling future high-precision optical clock networks. Furthermore, by exploiting the carrier phase, this approach is able to continuously track changes in the relative optical phase of distant optical oscillators to 9 mrad (7 as) at 1 s averaging, effectively extending optical phase coherence over a broad spatial network for applications such as correlated spectroscopy between distant atomic clocks.