| Summary: | <p>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 <sup>2</sup>S<sub>1/2</sub> (F 0) → <sup>2</sup>F<sub>7/2</sub> (F 3) electric octupole (E3) transition in <sup>171</sup>Yb<sup>+</sup>, with its Δν ≈ 1 nHz [4] linewidth and low sensitivity to external electromagnetic fields, lends itself to this usage [5]. </p> <p>We probe this transition in a single <sup>171</sup>Yb<sup>+</sup> 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 2<sup>nd</sup> order Doppler shifts of 3.6 × 10<sup>−19</sup>. Anomalous phonon heating rates in the radial plane were measured as (−4.9 ± 5.2) s<sup>−1</sup> and (−1.3 ± 3.6) s<sup>−1</sup> for secular frequencies of 446 kHz and 470 kHz. </p> <p>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. </p> <p>To pre-stabilize the frequency of our laser a 28 cm long, ultra-stable Fabry-Pérot 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<sup>−15</sup> (τ/1 s)<sup>−1/2</sup> was observed. The laser’s frequency was measured and its stability transferred to other wavelengths via a femtosecond optical frequency comb. </p> <p>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<sup>−16</sup>. </p> <p>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].</p>
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