Two $^{87}$Sr lattice clocks with $10^{-17}/\sqrt{\tau}$ level stability*

Optical lattice clocks have reached unprecedented precision by interrogating high-Q optical transitions with thousands of atoms simultaneously. The stability of optical lattice clocks is generally limited by the Dick effect, aliasing of the local oscillator's frequency noise. I detail the use of a laser stabilized to a 124 K silicon cavity to improve the stability of the JILA 1D and 3D $^{87}$Sr lattice clocks. The laser has a thermal-noise-limited stability of mod$\sigma = 4\times10^{-17}$, the current world record. Self-comparisons within each clock and asynchronous comparisons between the clocks demonstrate mid-$10^{-17}/\sqrt{\tau}$ stability for the 1D clock, and high-$10^{-17}/\sqrt{\tau}$ stability for the 3D clock. The 1D result is a record stability for a laser locked to a single atomic clock. I also discuss efforts to further improve the stability of the 3D clock by reducing its dead time.