Single-Ion Atomic Clock with 3 x 10-18 Systematic Uncertainty

We experimentally investigate an optical frequency standard based on the S-2(1/2)(F = 0) -> F-2(7/2)(F = 3) electric octupole (E3) transition of a single trapped Yb-171(+) ion. For the spectroscopy of this strongly forbidden transition, we utilize a Ramsey-type excitation scheme that provides immunity to probe-induced frequency shifts. The cancellation of these shifts is controlled by interleaved single-pulse Rabi spectroscopy, which reduces the related relative frequency uncertainty to 1.1 x 10(-18). To determine the frequency shift due to thermal radiation emitted by the ion's environment, we measure the static scalar differential polarizability of the E3 transition as 0.888(16) x 10(-40) J m(2)/V-2 and a dynamic correction eta(300 K) = -0.0015(7). This reduces the uncertainty due to thermal radiation to 1.8 x 10(-18). The residual motion of the ion yields the largest contribution (2.1 x 10(-18)) to the total systematic relative uncertainty of the clock of 3.2 x 10(-18).