An $^{27}$Al$^{+}$ quantum-logic clock with systematic uncertainty below $10^{-18}$

We describe an optical atomic clock based on quantum-logic spectroscopy of the $^1$S$_0$ $\leftrightarrow$ $^3$P$_0$ transition in $^{27}$Al$^{+}$ with a systematic uncertainty of $9.0 \times 10^{-19}$ and a frequency stability of $1.2 \times~10^{-15}/\sqrt{\tau}$. A $^{25}$Mg$^{+}$ ion is simultaneously trapped with the $^{27}$Al$^{+}$ ion and used for sympathetic cooling and state readout during clock operation. Improvements in a new trap have led to reduced secular motion heating, compared to previous $^{27}$Al$^{+}$ clocks, enabling clock operation with ion motion near the three-dimensional ground state. Operating the clock with a lower trap drive frequency has reduced excess micromotion, compared to previous $^{27}$Al$^{+}$ clocks, leading to a reduced time-dilation shift uncertainty. Other systematic uncertainties including those due to blackbody radiation and the second-order Zeeman effect have also been reduced. \footnote{Work supported by NIST, DARPA, and ONR. S.M.B. was supported by ARO through MURI grant W911NF-11-1-0400.}