High-precision comparison of two optical ion clocks for hundredfold improved bounds on Lorentz violation

We present a long-term frequency comparison over a period of six months between two optical clocks with single $^{171}$Yb$^{+}$ ions in separate ion traps, showing an agreement to within $3 \times 10^{-18}$. The two ions with their anisotropic electron momentum distributions in the metastable $^{2}F_{7/2}$ manifold are aligned along orthogonal quantization axes tilted with respect to Earth's axis of rotation. From the absence of an observed sidereal modulation of their frequency difference on the $2 \times 10^{-18}$ level we deduce limits on a possible violation of Lorentz symmetry for electrons (and photons) in the range of $10^{-21}$, an improvement on previous experiments [T. Pruttivarasin et al., Nature 517, 592 (2015)] by two orders of magnitude.