  A global network of optical atomic clocks will enable unprecedented
measurement precision in fields including tests of fundamental physics, dark
matter searches, geodesy, and navigation. Free-space laser links through the
turbulent atmosphere are needed to fully exploit this global network, by
enabling comparisons to airborne and spaceborne clocks. We demonstrate
frequency transfer over a 2.4 km atmospheric link with turbulence similar to
that of a ground-to-space link, achieving a fractional frequency stability of
6.1E-21 in 300 s of integration time. We also show that clock comparison
between ground and low Earth orbit will be limited by the stability of the
clocks themselves after only a few seconds of integration. This significantly
advances the technologies needed to realize a global timescale network of
optical atomic clocks.
