176Lu+ clock comparison at the 10-18 level via correlation spectroscopy

Abstract

The extreme precision of optical atomic clocks has led to an anticipated redefinition of the second by the International System of Units. Furthermore, accuracies pushing the boundary of 1 part in 10¹⁸ and beyond will enable new applications, such as in geodesy and tests of fundamental physics. The ¹S₀ to ³D₁ optical transition in ¹⁷⁶Lu⁺ has exceptionally low sensitivity to external perturbations, making it suitable for practical clock implementations with inaccuracy at or below 10^-18. Here, we perform high-accuracy comparisons between two ¹⁷⁶Lu⁺ references using correlation spectroscopy. A comparison at different magnetic fields is used to obtain a quadratic Zeeman coefficient of -4.89264(88) Hz/mT for the reference frequency. With a subsequent comparison at low field, we demonstrate agreement at the low 10^-18 level, statistically limited by the averaging time of 42 hours. The evaluated uncertainty in the frequency difference is 9 × 10^-19 and the lowest reported in comparing independent optical references.

Fig. 1.. ¹⁷⁶Lu⁺ spectroscopy.

(A) Atomic-level structure of ¹⁷⁶Lu⁺ showing the wavelengths of transitions used. (B) Levels of the 848-nm clock transition used in the clock interrogation sequence. Ω_α and ω_α denote the coupling strengths and frequencies for the fields driving the transitions indicated. (C) Clock interrogation sequence for HARS. An optional π-pulse on the optical transition is included when implementing hyper-Ramsey spectroscopy to suppress probe-induced ac-Stark shifts.

Fig. 2.. Measurements of the quadratic Zeeman coefficient (α_z).

Uncertainty budgets and parameters τ_L, τ₁, τ₂, T and static applied fields B₁ and B₂ for each experiment are given in the Supplementary Materials. Each point is the mean of all data collected at the given parameters, corrected for systematic errors, and offset by the weighted mean of all measurements. Error bars on the left represent the statistical uncertainty, and those on the right are inclusive of the systematic uncertainty. The shaded region indicates the uncertainty in the weighted mean. From all six measurements, we obtain the estimate α_z = −4.89264(88) Hz/mT², with ${\mathrm{\chi }}_{\nu }^2=1.30$.

Fig. 3.. Measurement instability.

Comparison data between two ¹⁷⁶Lu⁺ references implemented via HARS, including hyper-Ramsey for ac-Stark shift suppression (experiment 8). (A) Frequency difference measured over 42.4 hours in 10 runs of the experiment. Points are the mean of each run, and error bars are the statistical error determined by the projection noise limit. The dashed horizontal line is the weighted mean (${\mathrm{\chi }}_{\nu }^2=0.45$), and the shaded region is the corresponding uncertainty, which represents a fractional frequency difference of [−2.0 ± (3.7)_stat ± (0.9)_sys] × 10⁻¹⁸. (B) Fractional Allan deviation for the longest single run. The inset shows a typical parity signal as a function of the relative phase of the second π/2-pulse, the amplitude of which is limited by heating in Lu-1.