Optical clocks with accuracy validated at the 19th digit

Abstract

We report a comprehensive evaluation of all known sources of systematic uncertainty for two independent $^{176}$Lu$^+$ single-ion optical references, finding total systematic uncertainty of $1.1\times10^{-19}$ and $1.4\times10^{-19}$ for the two individual systems and $9.6\times10^{-20}$ for the difference. Through direct comparison via correlation spectroscopy, we demonstrate a relative frequency agreement of $-2.4\pm(5.7)_\mathrm{stat}\pm(1.0)_\mathrm{sys}\times10^{-19}$, where `stat' and `sys' indicate the statistical and systematic uncertainty, respectively. The comparison uncertainty is statistically limited after approximately 200 hours of averaging with a measurement instability of $4.8\times10^{-16}(τ/\mathrm{s})^{-1/2}$.

Figures (10)

• Figure 1: $^{176}$Lu$^+$ correlation spectroscopy (a) Simplified experimental scheme for correlation spectroscopy used to compare Lu-1 and Lu-2. Acousto-optic modulators (AOMs) labeled 1a and 2a control the intensity, frequency, and phase of clock laser pulses delivered to the respective trapped ions, while AOM 2b actively compensates for differential path length fluctuations referenced to retroreflecting mirrors near the viewports of the respective vacuum chambers. Microwaves are delivered by horns external to the vacuum chambers. (b) Atomic level structure of $^{176}$Lu$^+$ showing the wavelengths of transitions used. (c) The 848-nm optical clock transition and ${^3}D_{1}$ microwave clock transitions addressed in the clock interrogation sequence. $\Omega_\alpha$ and $f_\alpha$ denote the coupling strengths and frequencies for the fields driving the transitions indicated. (d) Clock interrogation sequence for hyperfine-averaged hyper-Ramsey spectroscopy. (e) Parity signal observed for a scan of the optical frequency difference with a Ramsey time $T_\mathrm{R} = 5\,$s.
• Figure 2: $^{176}$Lu$^+$ comparison results.a, Parity contrast inferred from the servo instability (points) compared to the simulated contrast loss due to ion heating (dashed black line) and due to uncorrelated $7\,$nT magnetic field flicker noise in both chambers (solid black line). b, Allan deviation for the longest continuous measurement with $T_\mathrm{R}=5$ s. The dashed line is the projection noise limit for full parity contrast ($C=1$) and the solid line is observed instability $4.8\times10^{-16} (\tau/\mathrm{s})^{-1/2}$ corresponding to $C=0.9$. c, Frequency difference (black points) from 11 measurements with a combined duration of 8.3 days over a 12.4 day interval (67% uptime). Shaded vertical bars show the measurement intervals, with the color indicating Ramsey time for $T_R=$ 5 s (blue), 7.5 s (orange), and 10 s (green). The weighted mean frequency difference is $[-2.4\pm(5.7)_\mathrm{stat}\pm(1.0)_\mathrm{sys}]\times10^{-19}$ with reduced chi squared $\chi_\nu^2 = 0.75$ for 10 degrees of freedom.
• Figure 3: Measurement of quadratic Zeeman coefficient. a, measured frequency difference with Lu-1 operated over a range of field amplitudes and Lu-2 at 0.1 mT. The coefficient $\alpha_z$ is determined from a quadratic fit (solid line). b, Residuals with respect to the quadratic fit, which have a reduced $\chi^2_\nu=0.4$ for 4 degrees of freedom. c, Three measurements of $\alpha_z$ over recent years. The 2023 measurement was reported in zhiqiang2023, the 2024 measurement is reported here, and the 2025 measurement is from the data shown in a,b. The vertical line and shaded area represent the combined value of $\alpha_z = -4.89327(51)\,\mathrm{Hz}/\mathrm{mT}^{2}$.
• Figure 4: Magnetic field instability. (blue) measurement of shorter time scale field instability without magnetic field compensation, (orange) instability inferred with magnetic field compensation from in-loop $|\,^3D_1,6,\pm1 \,\rangle$ Zeeman splitting measurements, and (green) independent measurement of magnetic field instability with magnetic field compensation but inferred from out-of-loop $|\,^3D_1,8,\pm1 \,\rangle$ Zeeman splitting measurements.
• Figure 5: a Detection sequence: (orange) $d_i$ are standard Bayesian state detection and $b_i$ high threshold fixed time detection, (red) 848 nm clock pulses of variable area for shelving, (blue) repump (350 nm, 622 nm, and 895 nm) pulse, and (light orange) laser cooling. b Probability of occurrence for outcome (i), first detected bright at $d_4$, and outcome (ii), first detected bright on $b_i$, as a function of Ramsey time for Lu-1 (blue points) and Lu-2 (orange points). Solid lines are linear fits to determine rates.