Fig. 1. Operational principle of optical clocks

Fig. 2. Absolute frequency measurement principle of optical clock

Fig. 3. Absolute frequency measurements of the optical transitions adopted as the secondary representations of the definition of the second [red shaded areas represent CIPM 2021 recommended frequency values and their corresponding uncertainties (they are not the result of a weighted average of the data in the figures)]. (a) Absolute frequency measurements of the ⁸⁷Sr optical lattice clock [JILA ^[67,93], LNE-SYRTE ^[68,92,94], NICT^[95-98], National Metrology Institute of Japan (NMIJ ^[99-100]),PTB^{[14,83,101-104]},NIM ^[104-105],NPL ^[106],UT ^{[69, 107]},and NTSC ^[89]]; (b) absolute frequency measurements of the ¹⁷¹Yb optical lattice clock [NIST ^[71,80], KRISS ^[14,108-111], Istituto Nazionale di Ricerca Metrologica (INRIM ^[112-114]), RIKEN ^[84,91,115], NMIJ ^[116-121], and ECNU ^[86]]; (c) absolute frequency measurements of the ¹⁷¹Yb⁺(E2) optical clock [PTB ^[122-127] and NPL ^[7,128]]; (d) absolute frequency measurements of the ¹⁷¹Yb⁺(E3) optical clock [PTB ^{[8,43,127, 129]} and NPL ^[7,130-133]]; (e) absolute frequency measurements of the ⁴⁰Ca⁺ optical clock [NICT ^[96,134], Universität Innsbruck (INNSBURK ^[135]), and APM ^[136-139]]; (f) absolute frequency measurements of the ⁸⁸Sr optical lattice clock [LNE-SYRTE ^[140], UT ^[141-142], Nicolaus Copernicus University (NCU ^[143]), University of Warsaw (UW^[144]), and PTB ^[70]]; (g) absolute frequency measurements of the ⁸⁸Sr⁺ optical clock (NRC ^[145-148] and NPL ^[63,149]); (h) absolute frequency measurements of the ²⁷Al⁺ optical clock (NIST ^[80,150-151]); (i) absolute frequency measurements of the ¹⁹⁹Hg optical lattice clock (LNE-SYRTE ^[37,85] and RIKEN ^[84,152]); (j) absolute frequency measurements of the ¹⁹⁹Hg⁺ optical clock (NIST ^[47,53,153])(names marked with an "*" indicates that their absolute frequencies are obtained by frequency ratio measurement between different optical clocks)

Table 1. Systematic uncertainty and stability of representative single-ion optical clocks in the domestic and overseas

Table 2. Systematic uncertainty and stability of representative optical lattice clocks in the domestic and overseas