Ytterbium lattice clock with systematic uncertainty of $1.3\times 10^{-18}$ and instability at the $10^{-19}$ level
We report an optical lattice clock based on $^{171}$Yb atoms with a total systematic uncertainty of $1.3\times 10^{-18}$. An in-vacuum buildup cavity was employed to enhance the lattice light power. Differential frequency measurement between two identical clocks facilitates the evaluation of systematic shifts. Synchronous comparison of the two clocks reached a stability level of $2.7\times 10^{-19}$ in an averaging time of 216,000~s. The blackbody radiation (BBR) shield which is placed in vacuum provides a well-characterized BBR environment, enabling an uncertainty contribution of $8.7\times 10^{-19}$ from the BBR Stark shift. Lattice light shifts were measured at different lattice depths $U$, and fitted with a fourth-order polynomial of $U$. The zero-linear-shift frequency $ν_{\mathrm{zero}}$ was determined to be 394 798 260.6(3) MHz. The lattice light shift can be controlled at an uncertainty level of $6.3\times 10^{-19}$ under typical operating conditions. Other systematic shifts have also been evaluated. The two clocks will be used for remote frequency comparisons between Shanghai and Wuhan.