Single-Ion Atomic Clock with \(3\times10^{-18}\) Systematic Uncertainty

Abstract

We experimentally investigate an optical frequency standard based on the \(^2S_{1/2} (F=0)\to {}^2F_{7/2} (F=3)\) electric octupole (\textit{E}3) transition of a single trapped \(^{171}\)Yb\(^+\) 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 \(1.1\times 10^{-18}\). To determine the frequency shift due to thermal radiation emitted by the ion's environment, we measure the static scalar differential polarizability of the \textit{E}3 transition as \(0.888(16)\times 10^{-40}\) J m\(^2\)/V\(^2\) and a dynamic correction \(\eta(300~\text{K})=-0.0015(7)\). This reduces the uncertainty due to thermal radiation to \(1.8\times 10^{-18}\). The residual motion of the ion yields the largest contribution \((2.1\times 10^{-18})\) to the total systematic relative uncertainty of the clock of \(3.2\times 10^{-18}\).