We report on a $^{88}$Sr$^+$ single-ion optical clock with an estimated fractional systematic uncertainty of $7.9 imes10^{-19}$. The low uncertainty is enabled by small rf losses, a thorough evaluation of the blackbody-radiation temperature, and our recent measurement of the differential polarizability. A detailed uncertainty evaluation is presented. We also report on two absolute frequency measurements: one against a remote cesium fountain clock, and one against International Atomic Time (TAI). The former lasted 12 d and resulted in a frequency value of 444 779 044 095 485.49(15) Hz. The latter spanned 10 months with monthly optical-clock uptimes between 68% and 99%, and yielded a frequency value of 444 779 044 095 485.373(44) Hz. With a fractional uncertainty of $9.8 imes10^{-17}$, it is, to our knowledge, the most accurate optical frequency measurement reported to date. Both frequency values are in agreement with other recent measurements, providing further evidence that the 2021 CIPM recommended frequency value is too high by 1.6 times its uncertainty.
Figures
16 panels with data across 8 figures. Each panel page shows the plot, its columns and its files; each data.csv begins with a header naming the paper, the panel, the source, the license and the provenance route.
Fig. 1
Illustrative figure, no extractable data. Shown in the paper PDF.
Fig. 2
panel (b): Measured Zeeman spectra at a magnetic field of 4.8 $\mu$T: excitation against detuning (kHz) as bars, with state preparation into $m_J = -1/2$ (blue) or $m_J = +1/2$ (red). The $S_{1/2}$ and $D_{5/2}$ sublevel labels printed below and above each peak are not drawn. data.csv
Fig. 3
panel (a): Clock self-comparison Allan deviation (ADEV) against averaging time $\tau$ (s), log-log: probe times 137 ms (circles), 137 ms EQS-free (crosses) and 202 ms (diamonds), with the slopes $2.7\times10^{-15}\,\tau^{-1/2}$ (dashed) and $2.0\times10^{-15}\,\tau^{-1/2}$ (dash-dot). data.csv
panel (b): Clock-transition line shape with 165 ms probe time: excitation probability against detuning (Hz), measured points (circles), the line-shape fit (solid) and the two probing points at $\pm\Delta f/2$ (dashed vertical segments). data.csv
Fig. 4
panel (b): Temperature rise $\Delta T$ (K) against squared rf voltage $V_{\mathrm{rf}}^2$ (kV$^2$) for parts 1 to 5 as labelled: measured points (circles) with error bars and fits of the form $k_{2}V_{\mathrm{rf}}^2 + k_{4}V_{\mathrm{rf}}^4$ (lines), and the simulated temperature rise seen by the ion (crosses, dashed). The dash-dotted line marks (350 V)$^2$. data.csv
Fig. 5
panel (c): Excitation (%) against optical detuning (Hz) at rf resonance for field direction 4, probe time 45 ms, drawn as a line through the measured points as printed. data.csv
Fig. 6
panel (a): Laser frequency offset measured by the ion (Hz) against time $t$ (h), one dot per point as printed. data.csv
panel (b): Laser drift (mHz/s) against time $t$ (h), evaluated from a third-order polynomial fit to the offset of panel (a). data.csv
panel (c): Fractional servo error /$10^{-16}$ against time $t$ (h), evaluated from the gain-corrected line center (noisy blue curve, mean of 100 cycles) and from Eq. (9) (red curve). data.csv
panel (d): Self-comparison Allan deviation (ADEV) against $\tau$ (s), log-log, using the normal clock data (blue circles) and the gain-corrected data (red crosses), with a $\tau^{-1/2}$ fit (dashed). data.csv
Fig. 7
panel (a): Fractional frequency deviation $y$ /$10^{-15}$ from the 2021 CIPM recommended value against MJD $-$ 60459, for the 5 d periods (dots) and the months (circles), both with error bars, and the full 10 months as a shaded $\pm1\sigma$ band. Vertical lines separate the Circular T periods 438 to 447; the period numbers printed above the data are not drawn. data.csv
panel (b): Fractional uptime of the Sr$^+$ clock against MJD $-$ 60459 for the 5 d periods (bars), the months (horizontal lines) and the full 10 months. The print shades the 10-month uptime as an area; here it is a horizontal line at that level. Vertical lines separate the Circular T periods. data.csv
Fig. 8
panel (1): Absolute frequency $\nu_0 - 444\,779\,044\,095\,000$ Hz of each labelled measurement with error bars: this work (circles), NRC (up triangles), PTB (diamond), NPL (down triangles) and the Sr$^+$/Yb$^+$ ratio value (square); line and band: CIPM 2021 value and uncertainty. Rotated from the print (rows along x). TAI 2005's bar exceeds the axis and is not drawn. data.csv
Fig. 9
panel (a): Hydrogen-maser fractional frequency $y_{\mathrm{HM}}$/$10^{-12}$ against MJD $-$ 60459, as measured against Sr$^+$ in 3600 s bins (dots) and against TAI as monthly values (circles). data.csv
panel (b): Residuals of a linear fit to the Sr$^+$ maser data, res./$10^{-15}$, against MJD $-$ 60459 (3600 s bins). data.csv
panel (c): Fractional-frequency power spectral density $S_y(f)$ (1/Hz) of the hydrogen maser against Fourier frequency $f$ (Hz), log-log: measured against Sr$^+$ and against 5 d TAI (solid lines) and the modelled maser noise (dashed). Where the Sr$^+$ curve leaves the top of the printed frame it is broken, as in the print. data.csv
panel (d): Monthly Sr$^+$ values $y$ /$10^{-15}$ against MJD $-$ 60459 with total uncertainties as error bars (circles), compared with interpolated values with extrapolation uncertainties as error bars (diamonds); the two are offset horizontally for clarity, as printed. data.csv
Cite
T. Lindvall, T. Fordell, K.J. Hanhijärvi, M. Doležal, J. Rahm, S. Weyers, A.E. Wallin. ⁸⁸Sr⁺ optical clock with 7.9×10⁻¹⁹ systematic uncertainty and measurement of its absolute frequency with 9.8×10⁻¹⁷ uncertainty. Phys. Rev. Appl. 24, 044082 (2025). https://doi.org/10.1103/czlf-bfvp
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