The combination of optical time transfer and optical clocks opens up the
possibility of large-scale free-space networks that connect both ground-based
optical clocks and future space-based optical clocks. Such networks promise
better tests of general relativity, dark matter searches, and gravitational
wave detection. The ability to connect optical clocks to a distant satellite
could enable space-based very long baseline interferometry (VLBI), advanced
satellite navigation, clock-based geodesy, and thousand-fold improvements in
intercontinental time dissemination. Thus far, only optical clocks have pushed
towards quantum-limited performance. In contrast, optical time transfer has not
operated at the analogous quantum limit set by the number of received photons.
Here, we demonstrate time transfer with near quantum-limited acquisition and
timing at 10,000 times lower received power than previous approaches. Over 300
km between mountaintops in Hawaii with launched powers as low as 40 μW,
distant timescales are synchronized to 320 attoseconds. This nearly
quantum-limited operation is critical for long-distance free-space links where
photons are few and amplification costly -- at 4.0 mW transmit power, this
approach can support 102 dB link loss, more than sufficient for future time
transfer to geosynchronous orbits