Comparing optical oscillators across the air to milliradians in phase and $10^{-17}$ in frequency

Abstract: 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 1.2x10$^{-17}$ at 1 second across a turbulent 4-km free space link, surpassing previous OTWTFT by 10-20x 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 attoseconds) at 1-sec averaging, effectively extending optical phase coherence over a broad spatial network for applications such as correlated spectroscopy between distant atomic clocks.