Single-Ion Atomic Clock with $3\times {10}^{-18}$ Systematic Uncertainty

We experimentally investigate an optical frequency standard based on the ${}^2{S}_{1/2}(F=0)\to {}^2{F}_{7/2}(F=3)$ electric octupole ($E3$) transition of a single trapped ${}^{171}{\mathrm{Yb}}^{+}$ 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 $E3$ transition as $0.888(16)\times {10}^{-40}\mathrm{J}{\mathrm{m}}^2/{\mathrm{V}}^2$ and a dynamic correction $\eta (300\mathrm{K})=-0.0015(7)$. 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 $3.2\times {10}^{-18}$.

Figure 1

(a) Error of the ${\mathrm{Yb}}^{+}$ clock frequency ${\nu }_{\text{clock}}$ in the realization of the unperturbed transition frequency ${\nu }_0$ as a function of an error ${\delta }_L$ in the estimate of the light shift for Rabi and for hyper-Ramsey spectroscopy (HRS). Here, Ramsey pulses of 30.5 ms and a free evolution period of 122 ms are assumed according to the experimental conditions. The very different sensitivities of ${\nu }_{\text{clock}}$ to ${\delta }_L$ allow one to engage a servo that uses the difference $ϵ$ between ${\nu }_{\text{clock}}$ obtained for Rabi spectroscopy and HRS as the discriminator signal. In (b) the instability (Allan deviation) of experimental $ϵ$ data is shown that follows $230\mathrm{Hz}/\tau (\mathrm{s})$ (dashed line) for $\tau \ge 1000\mathrm{s}$. The green solid line indicates the expected quantum projection noise limited combined instability of the ${\nu }_{\text{Rabi}}$ and ${\nu }_{\mathrm{HRS}}$ measurements of $7\mathrm{Hz}/\sqrt{\tau (\mathrm{s})}$.

Figure 2

Scalar electric differential polarizability $\mathrm{\Delta }{\alpha }_S$ of the ${}^2{S}_{1/2}(F=0)\to {}^2{F}_{7/2}(F=3)$ transition as a function of the wavelength of the perturbing radiation. The dashed and dotted lines are the results of calculations using theoretically predicted oscillator strengths, with the latter corrected by measured lifetimes. The square data point indicates the result of a previous measurement [20] and the filled circles indicate data obtained with near-infared laser radiation. The solid blue line is the result of a least-squares fit to the data (see text). The green shaded area shows the spectral distribution of room temperature blackbody radiation.

Figure 3

(a) Schematic of the setup used to determine the light shift profile. The mirror shown with dashed lines was installed after recording the profile to calibrate the position of the HeNe laser on the screen to a displacement of the beam waist position of the light-shifting laser (LS laser) at the position of the ion using a knife edge in front of a photodetector (PD). In (b) a light shift profile induced by the LS laser at $1.5\mu \mathrm{m}$ is depicted. The black dots correspond to the measurement positions and the surface plot is the result of a linear interpolation between these points.