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Many-particle optical lattice clocks have the potential for unprecedentedmeasurement precision and stability due to their low quantum projection noise.However, this potential has so far never been realized because clock stabilityhas been limited by frequency noise of optical local oscillators. Bysynchronously probing two 87Sr lattice systems using a laser with a thermalnoise floor of 1e-15, we remove classically correlated laser noise from theintercomparison, but this does not demonstrate independent clock performance.With an improved optical oscillator that has a 1e-16 thermal noise floor, wedemonstrate an order of magnitude improvement over the best reported stabilityof any independent clock, achieving a fractional instability of 1e-17 in 1000 sof averaging time for synchronous or asynchronous comparisons. This result iswithin a factor of 2 of the combined quantum projection noise limit for a 160ms probe time with ~10^3 atoms in each clock. We further demonstrate that evenat this high precision, the overall systematic uncertainty of our clock is notlimited by atomic interactions. For the second Sr clock, which has acavity-enhanced lattice, the atomic-density-dependent frequency shift isevaluated to be -3.11e-17 with an uncertainty of 8.2e-19.

Comparison of Two Independent Sr Optical Clocks with 1e-17 Stability at 10^3 s