  Rapid progress in the precision and accuracy of optical atomic clocks over
the last decade has advanced the frontiers of timekeeping, metrology, and
quantum science. However, the stabilities of most optical clocks remain limited
by the local oscillator rather than the atoms themselves, leaving room for
further progress. Here we implement a "multiplexed" one-dimensional optical
lattice clock, in which spatially-resolved, movable ensembles of ultra-cold
strontium atoms are trapped in the same optical lattice, interrogated
simultaneously by a shared clock laser, and read-out in parallel. By performing
synchronized Ramsey interrogations of ensemble pairs we observe atom-atom
coherence times up to 26 seconds, a 270-fold improvement over the atom-laser
coherence time, demonstrate a relative stability of
$9.7(4)\times10^{-18}/\sqrt{\tau}$ (where $\tau$ is the averaging time in
seconds), and reach a fractional uncertainty of $8.9(3)\times 10^{-20}$ after
3.3 hours of averaging. These results demonstrate that applications requiring
ultra-high-precision comparisons between optical atomic clocks need not be
limited by the stability of the local oscillator. With multiple ensemble pairs,
we realize a miniaturized clock network consisting of 6 atom ensembles,
resulting in 15 unique pairwise clock comparisons with relative stabilities
below $3\times10^{-17}/\sqrt{\tau}$. Finally, we demonstrate the capability to
simultaneously load spatially-resolved, heterogeneous ensemble pairs of all
four stable isotopes of strontium in a lattice. The unique capabilities offered
by this platform pave the way for future studies of precision isotope shift
measurements, spatially resolved characterization of limiting clock
systematics, development of clock-based gravitational wave and dark matter
detectors, and novel tests of relativity including measurements of the
gravitational redshift at sub-centimeter scales.
