  Improvements in atom-light coherence are foundational to progress in quantum
information science, quantum optics, and precision metrology. Optical atomic
clocks require local oscillators with exceptional optical coherence due to the
challenge of performing spectroscopy on their ultra-narrow linewidth clock
transitions. Advances in laser stabilization have thus enabled rapid progress
in clock precision. A new class of ultrastable lasers based on cryogenic
silicon reference cavities has recently demonstrated the longest optical
coherence times to date. In this work we utilize such a local oscillator, along
with a state-of-the-art frequency comb for coherence transfer, with two Sr
optical lattice clocks to achieve an unprecedented level of clock stability.
Through an anti-synchronous comparison, the fractional instability of both
clocks is assessed to be $4.8\times 10^{-17}/\sqrt{\tau}$ for an averaging time
$\tau$ in seconds. Synchronous interrogation reveals a quantum projection noise
dominated instability of $3.5(2)\times10^{-17}/\sqrt{\tau}$, resulting in a
precision of $5.8(3)\times 10^{-19}$ after a single hour of averaging. The
ability to measure sub-$10^{-18}$ level frequency shifts in such short
timescales will impact a wide range of applications for clocks in quantum
sensing and fundamental physics. For example, this precision allows one to
resolve the gravitational red shift from a 1 cm elevation change in only 20
minutes.
