27Al+ Quantum-Logic Clock with a Systematic Uncertainty below 10-18

We describe an optical atomic clock based on quantum-logic spectroscopy of the S-1(0) -> P-3(0) transition in Al-27(+) with a systematic uncertainty of 9.4 x 10(-19) and a frequency stability of 1.2 x 10(-15)/root tau.A Mg-25(+) ion is simultaneously trapped with the Al-27(+) ion and used for sympathetic cooling and state readout. Improvements in a new trap have led to reduced secular motion heating, compared to previous Al-27(+) clocks, enabling clock operation with ion secular motion near the three-dimensional ground state. Operating the clock with a lower trap drive frequency has reduced excess micromotion compared to previous Al-27(+) clocks. Both of these improvements have led 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.