Optical lattice clock: towards $10^{-17}$ uncertainty

Ultracold alkaine-earth atoms confined in an optical lattice are strong candidates for high-accuracy frequency standards and precision timekeepers. When last evaluated, the ytterbium optical lattice clock fractional uncertainty was $3.4\times10^{-16}$. Principle contributions to this uncertainty were the blackbody Stark effect, atomic cold-collisions, and lattice ac-Stark shifts not canceled at the magic wavelength balancing scalar Stark shifts in clock states $^1\!S_0$ and $^3\!P_0$. We report significant advances in these areas, paving the way toward a total uncertainty near the $10^{-17}$ level. We have since measured the clock static polarizability, reducing the blackbody Stark shift uncertainty to $3\times10^{-17}$, now limited by thermal environment uncertainty. Ultracold collisions between fermionic $^{171}$Yb atoms are dominated by p-wave interactions between $^1\!S_0$ and $^3\!P_0$ states. Ramsey spectroscopy with $\approx$~50\% excitation cancels density-dependent shifts at the $5\times10^{-18}$ level. We report progress measuring residual lattice ac-Stark shifts: polarizability away from the magic wavelength ($\propto I$, the lattice intensity), hyperpolarizability ($\propto I^2$) and multipole (M1-E2) effects ($\propto\sqrt{I}$).