Ytterbium optical lattice clock with $10^{-18}$ level characterization

A recent comparison of two ytterbium-based optical lattice clocks at NIST demonstrated record stability of $1.6$ parts in $10^{18}$ after 25,000s averaging. We report on measurements of the two primary systematic effects that shift the ultra-narrow clock transition, towards a reduction of the clock uncertainty to the $10^{-18}$ level. Uncertainty stemming from the blackbody radiation (BBR) shift is largely due to imprecise knowledge of the thermal environment surrounding the atoms. We detail the construction and operation of an in-vacuum, thermally-regulated radiation shield, which permits laser cooling and trapping while enabling an absolute temperature measurement with $<20$~mK precision. Additionally, while operation of the optical lattice at the magic wavelength ($\lambda_{\rm m}$) cancels the scalar Stark shift (since both clock states shift equally), higher-order vector and two-photon hyperpolarizability shifts remain. To evaluate these effects, as well as the polarizability away from $\lambda_{\rm m}$, we implement a lattice buildup cavity around the atoms. The resulting twenty-fold enhancement of the lattice intensity provides a significant lever arm for precise measurement of these effects.