Evaluation of the systematic shifts and absolute frequency measurement of a single Ca⁺ ion frequency standard

Abstract

This paper provides a detailed description of the ⁴⁰Ca⁺ optical frequency standard uncertainty evaluation and the absolute frequency measurement of the clock transition, as a summary and supplement for the published papers of Yao Huang et al. (Phys Rev A 84:053841, 1) and Huang et al. (Phys Rev A 85:030503, 2). The calculation of systematic frequency shifts, expected for a single trapped Ca⁺ ion optical frequency standard with a “clock” transition at 729 nm is described. There are several possible causes of systematic frequency shifts that need to be considered. In general, the frequency was measured with an uncertainty of 10⁻¹⁵ level, and the overall systematic shift uncertainty was reduced to below a part in 10⁻¹⁵. Several frequency shifts were calculated for the Ca⁺ ion optical frequency standard, including the trap design, optical and electromagnetic fields geometry and laboratory conditions, including the temperature condition and the altitude of the Ca⁺ ion. And we measured the absolute frequency of the 729-nm clock transition at the 10⁻¹⁵ level. An fs comb is referenced to a hydrogen maser, which is calibrated to the SI-second through the Global Positioning System (GPS). Using the GPS satellites as a link, we can calculate the frequency difference of the two hydrogen masers with a long distance, one in WIPM (Wuhan) and the other in National Institute of Metrology (NIM, Beijing). The frequency difference of the hydrogen maser in NIM (Beijing) and the SI-second calculated by BIPM is published on the BIPM web site every 1 month, with a time interval of every 5 days. By analyzing the experimental data obtained within 32 days of a total averaging time of >2 × 10⁶ s, the absolute frequency of the ⁴⁰Ca⁺ 4 s ² S _1/2–3d ²D_5/2 clock transition is measured as 411 042 129 776 393.0 (1.6) Hz with a fractional uncertainty of 3.9 × 10⁻¹⁵.