Frequency metrology at the 10⁻¹⁸ level with an ytterbium ion optical clock

Atomic clocks, the most accurate instruments in existence, are reaching new levels of precision. These devices now find novel uses—from the exploration of relativity [1] to the detection of dark matter [2, 3]—all from same principle: measurement of the frequency of the light that excites a reference atomic transition. The 2S1/2 (F 0) → 2F7/2 (F 3) electric octupole (E3) transition in 171Yb+, with its Δν ≈ 1 nHz [4] linewidth and low sensitivity to external electromagnetic fields, lends itself to this usage [5]. We probe this transition in a single 171Yb+ ion held in a newly-designed endcap RF trap [6]. This design achieves a low temperature rise of 0.14(14)K. Excess micromotion in the trap is automatically compensated, resulting in a fractional frequency uncertainty of the combined RF-Stark and 2nd order Doppler shifts of 3.6 × 10−19. Anomalous phonon heating rates in the radial plane were measured as (−4.9 ± 5.2) s−1 and (−1.3 ± 3.6) s−1 for secular frequencies of 446 kHz and 470 kHz. The ion’s differential polarisability at λ = 7 μm has been measured, suggesting a reduction in the BBR-related systematic error of the electric quadrupole (E2) transition by a factor of 5 and confirming the results of a previous measurement for the E3, performed using a different method [7]. However, a limitation prevented full confidence in our uncertainty levels. To pre-stabilize the frequency of our laser a 28 cm long, ultra-stable Fabry-Perot cavity was constructed and used to drive the E3 atomic resonance with a linewidth of 1.64(2) Hz. Its finesse was measured as 458 000 and, in an atomic lock, a clock stability of 1.9 × 10−15 (τ/1 s)−1/2 was observed. The laser’s frequency was measured and its stability transferred to other wavelengths via a femtosecond optical frequency comb. An international clock comparison campaign was carried out via satellite-mediated microwave links: the first of its scale, involving 4 National Measurement Institutes (NMIs) and 5 optical atomic clocks. A new technique was developed to analyse the resulting data and to characterize its uncertainty. The lowest fractional uncertainty in the comparison between any pair of clocks was 2.8 × 10−16. Finally, an absolute measurement of the E3 transition has been carried out through a link to International Atomic Time (TAI), without a local primary standard. The transition frequency was measured to be 642 121 496 772 645.17(22) Hz: the best measurement of this transition to date [8, 9].