Evaluation of an In+ Coulomb crystal clock with relative uncertainties in the low 10−18 range

Abstract

Clocks have been among the most accurate man-made devices for centuries. Atomic clocks, which have been defining time by means of a microwave transition in the 133Cs atom since 1967, represent a major step in this development. A redefinition of the SI unit of time based on optical atomic clocks is currently under discussion. This forthcoming redefinition requires, among other criteria, the repeated demonstration of the consistency of different optical frequency standards in the low 10−18 range. In this work, the first evaluation of the systematic shifts and their uncertainties in a 115In+–172Yb+ Coulomb crystal clock is presented. This clock utilizes the 1S0 ↔ 3P0 transition in 115In+. 172Yb+ ions are co-trapped with the 115In+ ions in a segmented Paul trap and used for sympathetic cooling. With a systematic uncertainty of 2.5×10−18 when operating with a 1In+–3Yb+ crystal and 2.6×10−18 when operating with a 2In+–4Yb+ crystal, this clock is one of the most accurate clocks in the world. In addition, the operation of the clock with multiple clock ions is the first of its kind at this level of uncertainty. Measurements with up to four clock ions show a reduction in instability from 1.6×10−15/√ τ for a single indium ion to 9.2(4)×10−16/√τ when operating with four indium ions. By using an additional quench laser, the instability in another series of measurements was reduced from a single-ion instability of 1.5×10−15/√ τ to a four-ion instability of 7.1(15)×10−16/√τ , which is consistent with the expected scaling of 1/√N with the number of clock ions N. In this work, the hyperfine structure of the 3P0 ↔ 1P1 transition used for quenching was also resolved for the first time and the hyperfine constants were determined to be AHFS = 265.42(75)MHz and BHFS = 291.4(135) MHz. In frequency comparisons with other clocks, the optical frequency ratios 115In+/171Yb+(E3) and 115In+/87Sr were determined. With a relative total uncertainty of 4.2 × 10−18, the former ratio is the most accurate frequency ratio of different species published to date. It is also the first to meet one of the requirements defined on the roadmap for redefining the SI unit of the second: Measurements of frequency ratios with relative total measurement uncertainties below 5 × 10−18. The determination of the absolute frequency results in an uncertainty of 1.3 × 10−16 for the 1S0 ↔ 3P0 transition in 115In+, which is limited by that of the cesium fountains. The results obtained summarized: ν115In+ ν171Yb+(E3) =1.973 773 591 557 215 788(8) ν115In+ ν87Sr =2.952 748 749 874 860 781(27) ν115In+ =1 267 402 452 901 038.87(16) Hz