<table><caption>**Table B1.** Frequency ratios consistent with the 2021 recommended frequency values, taking into account the covariance of the output matrix. ($\nu_2$ and $\nu_9$ are linked to the other frequencies only via Cs ($\nu_{15}$), and hence are not included in this table.).</caption><thead><tr><th>Clock transitions</th><th>Atomic species</th><th>Frequency ratio</th><th>Fractional uncertainty</th></tr></thead><tbody><tr><td>ν<sub>1</sub>/ν<sub>3</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>199</sup>Hg</td><td>1.123 010 988 476 8743(49)</td><td>4.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>1</sub>/ν<sub>4</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>27</sup>Al<sup>+</sup></td><td>1.130 584 343 961 8487(49)</td><td>4.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>1</sub>/ν<sub>5</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>199</sup>Hg<sup>+</sup></td><td>1.190 360 410 756 6604(51)</td><td>4.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>1</sub>/ν<sub>6</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>171</sup>Yb<sup>+</sup> (E2)</td><td>1.841 194 044 091 2659(80)</td><td>4.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>1</sub>/ν<sub>7</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>171</sup>Yb<sup>+</sup> (E3)</td><td>1.973 773 591 557 2195(85)</td><td>4.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>1</sub>/ν<sub>8</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>171</sup>Yb</td><td>2.445 326 324 126 955(11)</td><td>4.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>1</sub>/ν<sub>10</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>88</sup>Sr<sup>+</sup></td><td>2.849 510 267 459 795(13)</td><td>4.5 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>1</sub>/ν<sub>11</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>88</sup>Sr</td><td>2.952 748 322 069 815(13)</td><td>4.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>1</sub>/ν<sub>12</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>87</sup>Sr</td><td>2.952 748 749 874 866(13)</td><td>4.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>1</sub>/ν<sub>13</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>40</sup>Ca<sup>+</sup></td><td>3.083 388 200 597 554(14)</td><td>4.7 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>1</sub>/ν<sub>14</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>87</sup>Rb</td><td>185 436.914 199 787 30(80)</td><td>4.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>3</sub>/ν<sub>4</sub></td><td><sup>199</sup>Hg/<sup>27</sup>Al<sup>+</sup></td><td>1.006 743 794 640 198 49(15)</td><td>1.5 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>3</sub>/ν<sub>5</sub></td><td><sup>199</sup>Hg/<sup>199</sup>Hg<sup>+</sup></td><td>1.059 972 184 574 196 57(19)</td><td>1.8 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>3</sub>/ν<sub>6</sub></td><td><sup>199</sup>Hg/<sup>171</sup>Yb<sup>+</sup> (E2)</td><td>1.639 515 608 470 095 42(28)</td><td>1.7 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>3</sub>/ν<sub>7</sub></td><td><sup>199</sup>Hg/<sup>171</sup>Yb<sup>+</sup> (E3)</td><td>1.757 572 821 468 313 31(27)</td><td>1.5 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>3</sub>/ν<sub>8</sub></td><td><sup>199</sup>Hg/<sup>171</sup>Yb</td><td>2.177 473 194 134 564 88(32)</td><td>1.5 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>3</sub>/ν<sub>10</sub></td><td><sup>199</sup>Hg/<sup>88</sup>Sr<sup>+</sup></td><td>2.537 384 136 663 3019(34)</td><td>1.4 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>3</sub>/ν<sub>11</sub></td><td><sup>199</sup>Hg/<sup>88</sup>Sr</td><td>2.629 313 828 954 238 79(40)</td><td>1.5 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>3</sub>/ν<sub>12</sub></td><td><sup>199</sup>Hg/<sup>87</sup>Sr</td><td>2.629 314 209 898 909 56(39)</td><td>1.5 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>3</sub>/ν<sub>13</sub></td><td><sup>199</sup>Hg/<sup>40</sup>Ca<sup>+</sup></td><td>2.745 643 838 071 0009(49)</td><td>1.8 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>3</sub>/ν<sub>14</sub></td><td><sup>199</sup>Hg/<sup>87</sup>Rb</td><td>165 124.754 879 997 262(60)</td><td>3.6 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>4</sub>/ν<sub>5</sub></td><td><sup>27</sup>Al<sup>+</sup>/<sup>199</sup>Hg<sup>+</sup></td><td>1.052 871 833 148 990 45(11)</td><td>1.0 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>4</sub>/ν<sub>6</sub></td><td><sup>27</sup>Al<sup>+</sup>/<sup>171</sup>Yb<sup>+</sup> (E2)</td><td>1.628 533 115 573 902 39(14)</td><td>8.3 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>4</sub>/ν<sub>7</sub></td><td><sup>27</sup>Al<sup>+</sup>/<sup>171</sup>Yb<sup>+</sup> (E3)</td><td>1.745 799 508 102 709 104(84)</td><td>4.8 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>4</sub>/ν<sub>8</sub></td><td><sup>27</sup>Al<sup>+</sup>/<sup>171</sup>Yb</td><td>2.162 887 127 516 663 705(24)</td><td>1.1 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>4</sub>/ν<sub>10</sub></td><td><sup>27</sup>Al<sup>+</sup>/<sup>88</sup>Sr<sup>+</sup></td><td>2.520 387 163 220 7488(34)</td><td>1.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>4</sub>/ν<sub>11</sub></td><td><sup>27</sup>Al<sup>+</sup>/<sup>88</sup>Sr</td><td>2.611 701 053 388 596 03(10)</td><td>3.9 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>4</sub>/ν<sub>12</sub></td><td><sup>27</sup>Al<sup>+</sup>/<sup>87</sup>Sr</td><td>2.611 701 431 781 463 019(39)</td><td>1.5 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>4</sub>/ν<sub>13</sub></td><td><sup>27</sup>Al<sup>+</sup>/<sup>40</sup>Ca<sup>+</sup></td><td>2.727 251 811 919 3078(48)</td><td>1.8 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>4</sub>/ν<sub>14</sub></td><td><sup>27</sup>Al<sup>+</sup>/<sup>87</sup>Rb</td><td>164 018.646 808 755 766(54)</td><td>3.3 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>5</sub>/ν<sub>6</sub></td><td><sup>199</sup>Hg<sup>+</sup>/<sup>171</sup>Yb<sup>+</sup> (E2)</td><td>1.546 753 426 486 100 05(21)</td><td>1.3 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>5</sub>/ν<sub>7</sub></td><td><sup>199</sup>Hg<sup>+</sup>/<sup>171</sup>Yb<sup>+</sup> (E3)</td><td>1.658 131 078 387 072 22(19)</td><td>1.1 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>5</sub>/ν<sub>8</sub></td><td><sup>199</sup>Hg<sup>+</sup>/<sup>171</sup>Yb</td><td>2.054 273 900 601 723 59(22)</td><td>1.0 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>5</sub>/ν<sub>10</sub></td><td><sup>199</sup>Hg<sup>+</sup>/<sup>88</sup>Sr<sup>+</sup></td><td>2.393 821 435 684 7480(32)</td><td>1.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>5</sub>/ν<sub>11</sub></td><td><sup>199</sup>Hg<sup>+</sup>/<sup>88</sup>Sr</td><td>2.480 549 836 324 681 89(28)</td><td>1.1 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>5</sub>/ν<sub>12</sub></td><td><sup>199</sup>Hg<sup>+</sup>/<sup>87</sup>Sr</td><td>2.480 550 195 715 877 54(26)</td><td>1.1 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>5</sub>/ν<sub>13</sub></td><td><sup>199</sup>Hg<sup>+</sup>/<sup>40</sup>Ca<sup>+</sup></td><td>2.590 298 007 842 4970(46)</td><td>1.8 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>5</sub>/ν<sub>14</sub></td><td><sup>199</sup>Hg<sup>+</sup>/<sup>87</sup>Rb</td><td>155 782.158 516 102 797(54)</td><td>3.5 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>6</sub>/ν<sub>7</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E2)/<sup>171</sup>Yb<sup>+</sup> (E3)</td><td>1.072 007 373 634 205 473(73)</td><td>6.9 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>6</sub>/ν<sub>8</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E2)/<sup>171</sup>Yb</td><td>1.328 119 831 787 671 42(11)</td><td>8.3 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>6</sub>/ν<sub>10</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E2)/<sup>88</sup>Sr<sup>+</sup></td><td>1.547 642 561 958 3136(21)</td><td>1.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>6</sub>/ν<sub>11</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E2)/<sup>88</sup>Sr</td><td>1.603 713 813 623 139 52(14)</td><td>8.9 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>6</sub>/ν<sub>12</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E2)/<sup>87</sup>Sr</td><td>1.603 714 045 975 103 00(13)</td><td>8.2 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>6</sub>/ν<sub>13</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E2)/<sup>40</sup>Ca<sup>+</sup></td><td>1.674 667 703 001 0606(30)</td><td>1.8 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>6</sub>/ν<sub>14</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E2)/<sup>87</sup>Rb</td><td>100 715.573 567 538 329(34)</td><td>3.4 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>7</sub>/ν<sub>8</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E3)/<sup>171</sup>Yb</td><td>1.238 909 231 832 259 428(59)</td><td>4.7 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>7</sub>/ν<sub>10</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E3)/<sup>88</sup>Sr<sup>+</sup></td><td>1.443 686 489 498 3514(19)</td><td>1.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>7</sub>/ν<sub>11</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E3)/<sup>88</sup>Sr</td><td>1.495 991 401 800 156 824(86)</td><td>5.8 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>7</sub>/ν<sub>12</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E3)/<sup>87</sup>Sr</td><td>1.495 991 618 544 900 552(68)</td><td>4.6 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>7</sub>/ν<sub>13</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E3)/<sup>40</sup>Ca<sup>+</sup></td><td>1.562 179 276 177 7189(28)</td><td>1.8 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>7</sub>/ν<sub>14</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E3)/<sup>87</sup>Rb</td><td>93 950.448 518 001 415(31)</td><td>3.3 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>8</sub>/ν<sub>10</sub></td><td><sup>171</sup>Yb<sup>+</sup>/<sup>88</sup>Sr<sup>+</sup></td><td>1.165 288 345 913 1553(16)</td><td>1.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>8</sub>/ν<sub>11</sub></td><td><sup>171</sup>Yb<sup>+</sup>/<sup>88</sup>Sr</td><td>1.207 506 864 395 296 327(46)</td><td>3.8 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>8</sub>/ν<sub>12</sub></td><td><sup>171</sup>Yb<sup>+</sup>/<sup>87</sup>Sr</td><td>1.207 507 039 343 337 845(16)</td><td>1.3 × 10<sup>-17</sup></td></tr></tbody></table>

(Continued.)
<table><caption>**Table B1.** Frequency ratios consistent with the 2021 recommended frequency values, taking into account the covariance of the output matrix. ($\nu_2$ and $\nu_9$ are linked to the other frequencies only via Cs ($\nu_{15}$), and hence are not included in this table.).</caption><thead><tr><th>Clock transitions</th><th>Atomic species</th><th>Frequency ratio</th><th>Fractional uncertainty</th></tr></thead><tbody><tr><td>ν<sub>1</sub>/ν<sub>3</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>199</sup>Hg</td><td>1.123 010 988 476 8743(49)</td><td>4.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>1</sub>/ν<sub>4</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>27</sup>Al<sup>+</sup></td><td>1.130 584 343 961 8487(49)</td><td>4.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>1</sub>/ν<sub>5</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>199</sup>Hg<sup>+</sup></td><td>1.190 360 410 756 6604(51)</td><td>4.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>1</sub>/ν<sub>6</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>171</sup>Yb<sup>+</sup> (E2)</td><td>1.841 194 044 091 2659(80)</td><td>4.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>1</sub>/ν<sub>7</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>171</sup>Yb<sup>+</sup> (E3)</td><td>1.973 773 591 557 2195(85)</td><td>4.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>1</sub>/ν<sub>8</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>171</sup>Yb</td><td>2.445 326 324 126 955(11)</td><td>4.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>1</sub>/ν<sub>10</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>88</sup>Sr<sup>+</sup></td><td>2.849 510 267 459 795(13)</td><td>4.5 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>1</sub>/ν<sub>11</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>88</sup>Sr</td><td>2.952 748 322 069 815(13)</td><td>4.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>1</sub>/ν<sub>12</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>87</sup>Sr</td><td>2.952 748 749 874 866(13)</td><td>4.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>1</sub>/ν<sub>13</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>40</sup>Ca<sup>+</sup></td><td>3.083 388 200 597 554(14)</td><td>4.7 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>1</sub>/ν<sub>14</sub></td><td><sup>115</sup>In<sup>+</sup>/<sup>87</sup>Rb</td><td>185 436.914 199 787 30(80)</td><td>4.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>3</sub>/ν<sub>4</sub></td><td><sup>199</sup>Hg/<sup>27</sup>Al<sup>+</sup></td><td>1.006 743 794 640 198 49(15)</td><td>1.5 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>3</sub>/ν<sub>5</sub></td><td><sup>199</sup>Hg/<sup>199</sup>Hg<sup>+</sup></td><td>1.059 972 184 574 196 57(19)</td><td>1.8 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>3</sub>/ν<sub>6</sub></td><td><sup>199</sup>Hg/<sup>171</sup>Yb<sup>+</sup> (E2)</td><td>1.639 515 608 470 095 42(28)</td><td>1.7 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>3</sub>/ν<sub>7</sub></td><td><sup>199</sup>Hg/<sup>171</sup>Yb<sup>+</sup> (E3)</td><td>1.757 572 821 468 313 31(27)</td><td>1.5 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>3</sub>/ν<sub>8</sub></td><td><sup>199</sup>Hg/<sup>171</sup>Yb</td><td>2.177 473 194 134 564 88(32)</td><td>1.5 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>3</sub>/ν<sub>10</sub></td><td><sup>199</sup>Hg/<sup>88</sup>Sr<sup>+</sup></td><td>2.537 384 136 663 3019(34)</td><td>1.4 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>3</sub>/ν<sub>11</sub></td><td><sup>199</sup>Hg/<sup>88</sup>Sr</td><td>2.629 313 828 954 238 79(40)</td><td>1.5 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>3</sub>/ν<sub>12</sub></td><td><sup>199</sup>Hg/<sup>87</sup>Sr</td><td>2.629 314 209 898 909 56(39)</td><td>1.5 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>3</sub>/ν<sub>13</sub></td><td><sup>199</sup>Hg/<sup>40</sup>Ca<sup>+</sup></td><td>2.745 643 838 071 0009(49)</td><td>1.8 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>3</sub>/ν<sub>14</sub></td><td><sup>199</sup>Hg/<sup>87</sup>Rb</td><td>165 124.754 879 997 262(60)</td><td>3.6 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>4</sub>/ν<sub>5</sub></td><td><sup>27</sup>Al<sup>+</sup>/<sup>199</sup>Hg<sup>+</sup></td><td>1.052 871 833 148 990 45(11)</td><td>1.0 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>4</sub>/ν<sub>6</sub></td><td><sup>27</sup>Al<sup>+</sup>/<sup>171</sup>Yb<sup>+</sup> (E2)</td><td>1.628 533 115 573 902 39(14)</td><td>8.3 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>4</sub>/ν<sub>7</sub></td><td><sup>27</sup>Al<sup>+</sup>/<sup>171</sup>Yb<sup>+</sup> (E3)</td><td>1.745 799 508 102 709 104(84)</td><td>4.8 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>4</sub>/ν<sub>8</sub></td><td><sup>27</sup>Al<sup>+</sup>/<sup>171</sup>Yb</td><td>2.162 887 127 516 663 705(24)</td><td>1.1 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>4</sub>/ν<sub>10</sub></td><td><sup>27</sup>Al<sup>+</sup>/<sup>88</sup>Sr<sup>+</sup></td><td>2.520 387 163 220 7488(34)</td><td>1.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>4</sub>/ν<sub>11</sub></td><td><sup>27</sup>Al<sup>+</sup>/<sup>88</sup>Sr</td><td>2.611 701 053 388 596 03(10)</td><td>3.9 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>4</sub>/ν<sub>12</sub></td><td><sup>27</sup>Al<sup>+</sup>/<sup>87</sup>Sr</td><td>2.611 701 431 781 463 019(39)</td><td>1.5 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>4</sub>/ν<sub>13</sub></td><td><sup>27</sup>Al<sup>+</sup>/<sup>40</sup>Ca<sup>+</sup></td><td>2.727 251 811 919 3078(48)</td><td>1.8 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>4</sub>/ν<sub>14</sub></td><td><sup>27</sup>Al<sup>+</sup>/<sup>87</sup>Rb</td><td>164 018.646 808 755 766(54)</td><td>3.3 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>5</sub>/ν<sub>6</sub></td><td><sup>199</sup>Hg<sup>+</sup>/<sup>171</sup>Yb<sup>+</sup> (E2)</td><td>1.546 753 426 486 100 05(21)</td><td>1.3 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>5</sub>/ν<sub>7</sub></td><td><sup>199</sup>Hg<sup>+</sup>/<sup>171</sup>Yb<sup>+</sup> (E3)</td><td>1.658 131 078 387 072 22(19)</td><td>1.1 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>5</sub>/ν<sub>8</sub></td><td><sup>199</sup>Hg<sup>+</sup>/<sup>171</sup>Yb</td><td>2.054 273 900 601 723 59(22)</td><td>1.0 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>5</sub>/ν<sub>10</sub></td><td><sup>199</sup>Hg<sup>+</sup>/<sup>88</sup>Sr<sup>+</sup></td><td>2.393 821 435 684 7480(32)</td><td>1.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>5</sub>/ν<sub>11</sub></td><td><sup>199</sup>Hg<sup>+</sup>/<sup>88</sup>Sr</td><td>2.480 549 836 324 681 89(28)</td><td>1.1 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>5</sub>/ν<sub>12</sub></td><td><sup>199</sup>Hg<sup>+</sup>/<sup>87</sup>Sr</td><td>2.480 550 195 715 877 54(26)</td><td>1.1 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>5</sub>/ν<sub>13</sub></td><td><sup>199</sup>Hg<sup>+</sup>/<sup>40</sup>Ca<sup>+</sup></td><td>2.590 298 007 842 4970(46)</td><td>1.8 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>5</sub>/ν<sub>14</sub></td><td><sup>199</sup>Hg<sup>+</sup>/<sup>87</sup>Rb</td><td>155 782.158 516 102 797(54)</td><td>3.5 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>6</sub>/ν<sub>7</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E2)/<sup>171</sup>Yb<sup>+</sup> (E3)</td><td>1.072 007 373 634 205 473(73)</td><td>6.9 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>6</sub>/ν<sub>8</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E2)/<sup>171</sup>Yb</td><td>1.328 119 831 787 671 42(11)</td><td>8.3 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>6</sub>/ν<sub>10</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E2)/<sup>88</sup>Sr<sup>+</sup></td><td>1.547 642 561 958 3136(21)</td><td>1.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>6</sub>/ν<sub>11</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E2)/<sup>88</sup>Sr</td><td>1.603 713 813 623 139 52(14)</td><td>8.9 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>6</sub>/ν<sub>12</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E2)/<sup>87</sup>Sr</td><td>1.603 714 045 975 103 00(13)</td><td>8.2 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>6</sub>/ν<sub>13</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E2)/<sup>40</sup>Ca<sup>+</sup></td><td>1.674 667 703 001 0606(30)</td><td>1.8 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>6</sub>/ν<sub>14</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E2)/<sup>87</sup>Rb</td><td>100 715.573 567 538 329(34)</td><td>3.4 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>7</sub>/ν<sub>8</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E3)/<sup>171</sup>Yb</td><td>1.238 909 231 832 259 428(59)</td><td>4.7 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>7</sub>/ν<sub>10</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E3)/<sup>88</sup>Sr<sup>+</sup></td><td>1.443 686 489 498 3514(19)</td><td>1.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>7</sub>/ν<sub>11</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E3)/<sup>88</sup>Sr</td><td>1.495 991 401 800 156 824(86)</td><td>5.8 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>7</sub>/ν<sub>12</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E3)/<sup>87</sup>Sr</td><td>1.495 991 618 544 900 552(68)</td><td>4.6 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>7</sub>/ν<sub>13</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E3)/<sup>40</sup>Ca<sup>+</sup></td><td>1.562 179 276 177 7189(28)</td><td>1.8 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>7</sub>/ν<sub>14</sub></td><td><sup>171</sup>Yb<sup>+</sup> (E3)/<sup>87</sup>Rb</td><td>93 950.448 518 001 415(31)</td><td>3.3 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>8</sub>/ν<sub>10</sub></td><td><sup>171</sup>Yb<sup>+</sup>/<sup>88</sup>Sr<sup>+</sup></td><td>1.165 288 345 913 1553(16)</td><td>1.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>8</sub>/ν<sub>11</sub></td><td><sup>171</sup>Yb<sup>+</sup>/<sup>88</sup>Sr</td><td>1.207 506 864 395 296 327(46)</td><td>3.8 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>8</sub>/ν<sub>12</sub></td><td><sup>171</sup>Yb<sup>+</sup>/<sup>87</sup>Sr</td><td>1.207 507 039 343 337 845(16)</td><td>1.3 × 10<sup>-17</sup></td></tr></tbody></table>

(Continued.)
<table><caption>Table B1. (Continued.)</caption><thead><tr><th>Clock transitions</th><th>Atomic species</th><th>Frequency ratio</th><th>Fractional uncertainty</th></tr></thead><tbody><tr><td>ν<sub>8</sub>/ν<sub>13</sub></td><td><sup>171</sup>Yb/<sup>40</sup>Ca<sup>+</sup></td><td>1.260 931 177 231 8993(22)</td><td>1.8 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>8</sub>/ν<sub>14</sub></td><td><sup>171</sup>Yb/<sup>87</sup>Rb</td><td>75 833.197 545 114 200(25)</td><td>3.3 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>10</sub>/ν<sub>11</sub></td><td><sup>88</sup>Sr<sup>+</sup>/<sup>88</sup>Sr</td><td>1.036 230 104 446 0007(14)</td><td>1.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>10</sub>/ν<sub>12</sub></td><td><sup>88</sup>Sr<sup>+</sup>/<sup>87</sup>Sr</td><td>1.036 230 254 578 8345(14)</td><td>1.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>10</sub>/ν<sub>13</sub></td><td><sup>88</sup>Sr<sup>+</sup>/<sup>40</sup>Ca<sup>+</sup></td><td>1.082 076 536 381 8990(24)</td><td>2.2 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>10</sub>/ν<sub>14</sub></td><td><sup>88</sup>Sr<sup>+</sup>/<sup>87</sup>Rb</td><td>65 076.766 459 625 929(88)</td><td>1.4 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>11</sub>/ν<sub>12</sub></td><td><sup>88</sup>Sr/<sup>87</sup>Sr</td><td>1.000 000 144 883 682 799(36)</td><td>3.6 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>11</sub>/ν<sub>13</sub></td><td><sup>88</sup>Sr/<sup>40</sup>Ca<sup>+</sup></td><td>1.044 243 485 823 4592(18)</td><td>1.8 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>11</sub>/ν<sub>14</sub></td><td><sup>88</sup>Sr/<sup>87</sup>Rb</td><td>62 801.462 899 418 361(21)</td><td>3.3 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>12</sub>/ν<sub>13</sub></td><td><sup>87</sup>Sr/<sup>40</sup>Ca<sup>+</sup></td><td>1.044 243 334 529 6392(18)</td><td>1.8 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>12</sub>/ν<sub>14</sub></td><td><sup>87</sup>Sr/<sup>87</sup>Rb</td><td>62 801.453 800 512 449(21)</td><td>3.3 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>13</sub>/ν<sub>14</sub></td><td><sup>40</sup>Ca<sup>+</sup>/<sup>87</sup>Rb</td><td>60 140.631 712 818 40(11)</td><td>1.8 × 10<sup>-15</sup></td></tr></tbody></table>

ORCID iDs

H S Margolis https://orcid.org/0000-0002-8991-3855

G Petit https://orcid.org/0000-0002-6837-3052

C Oates https://orcid.org/0000-0001-7842-8259

T Ido https://orcid.org/0000-0003-3500-6042

S Bize https://orcid.org/0000-0003-2483-5152

References

[1] Riehle F, Gill P, Arias F and Robertsson L 2018 The CIPM list of recommended frequency standard values: guidelines and procedures *Metrologia* **55** 188–200

[2] Terms of reference for the CCL-CCTF Working Group on Frequency Standards (WGFS) (available at: www.bipm.org/en/committees/cc/cctf/wg/ccl-cctf-wgfs)

[3] Consultative Committee for Time and Frequency 2021 Recommendation CCTF PSFS 2 (2021): updates to the CIPM list of standard frequencies (available at: www.bipm.org/en/committees/cc/cctf/22_2-2021)

[4] BIPM 2021 Recommended values of standard frequencies (available at: www.bipm.org/en/publications/mises-en-pratique/standard-frequencies.html)

[5] Petit G, Arias F and Panfilo G 2015 International atomic time: status and future challenges *C. R. Physique* **16** 480–8

[6] Panfilo G and Arias F 2019 The Coordinated universal Time (UTC) *Metrologia* **56** 042001

[7] Primary and Secondary Frequency Standards participating to TAI (available at: https://webtai.bipm.org/ftp/pub/tai/data/PSFS_reports/)

[8] Margolis H S and Gill P 2015 Least-squares analysis of clock frequency comparison data to deduce optimized frequency and frequency ratio values *Metrologia* **52** 628–34

[9] Robertsson L 2016 On the evaluation of ultra-high-precision frequency ratio measurements: examining closed loops in a graph theory framework *Metrologia* **53** 1272–80

[10] Margolis H S and Gill P 2016 Determination of optimized frequency and frequency ratio values from over-determined sets of clock comparison data *J. Phys.: Conf. Ser.* **723** 012060

[11] Mohr P J and Taylor B N 2000 CODATA recommended values of the fundamental physical constants: 1998 *Rev. Mod. Phys.* **72** 351–495

[12] von Zanthier J et al 2000 Absolute frequency measurement of the $\text{In}^+$ clock transition with a mode-locked laser *Opt. Lett.* **25** 1729–31

[13] Wang Y H, Dumke R, Liu T, Stejskal A, Zhao Y N, Zhang J, Lu Z H, Wang L J, Becker T and Walther H 2007 Absolute frequency measurement and high resolution spectroscopy of $^{115}\text{In}^+$ $5\text{s}^2 \text{1}\text{S}_0-5\text{s}5\text{p} \text{3}\text{P}_0$ narrowline transition *Opt. Commun.* **273** 526–31

[14] Ohtsubo N, Li Y, Matsubara K, Ido T and Hayasaka K 2017 Frequency measurement of the clock transition of an indium ion sympathetically-cooled in a linear trap *Opt. Express* **25** 11725–35

[15] Parthey C G et al 2011 Improved measurement of the hydrogen 1S–2S transition frequency *Phys. Rev. Lett.* **107** 203001

[16] Matveev A et al 2013 Precision measurement of the hydrogen 1S–2S frequency via a 920 km fiber link *Phys. Rev. Lett.* **110** 230801

[17] McFerran J J, Yi L, Mejri S, Di Manno S, Zhang W, Guéna J, Le Coq Y and Bize S 2012 Neutral atom frequency reference in the deep ultraviolet with fractional uncertainty = $5.7 \times 10^{-15}$ *Phys. Rev. Lett.* **108** 183004

[18] McFerran J J, Yi L, Mejri S, Di Manno S, Zhang W, Guéna J, Le Coq Y and Bize S 2015 Erratum: Neutral atom frequency reference in the deep ultraviolet with fractional uncertainty = $5.7 \times 10^{-15}$ [Phys. Rev. Lett. 108, 183004 (2012)] *Phys. Rev. Lett.* **115** 219901

[19] Tyumenev R et al 2016 Comparing a mercury optical lattice clock with microwave and optical frequency standards *New J. Phys.* **18** 113002

[20] Rosenband T et al 2007 Observation of the $^{1}\text{S}_0 \rightarrow ^3\text{P}_0$ clock transition in $^{27}\text{Al}^+$ *Phys. Rev. Lett.* **98** 220801

[21] Stalnaker J E et al 2007 Optical-to-microwave frequency comparison with fractional uncertainty of $10^{-15}$ *Appl. Phys. B* **89** 167–76

[22] Consultative Committee for Length 2005 *Report of the 12th Meeting, Consultative Committee for Length (CCL) (15–16 September 2005)* (available at: www.bipm.org/documents/20126/31697125/12th+meeting/058b3c8a-8914-18c1-3fe1-2e601dcbdfad)

[23] Tamm C, Weyers S, Lipphardt B and Peik E 2009 Stray-field-induced quadrupole shift and absolute frequency of the 688-THz $^{171}\text{Yb}^+$ single-ion optical frequency standard *Phys. Rev. A* **80** 043403

[24] Webster S, Godun R, King S, Huang G, Walton B, Tsatourian V, Margolis H, Lea S and Gill P 2010 Frequency measurement of the $^{2}\text{S}_{1/2} \rightarrow ^2\text{D}_{3/2}$ electric quadrupole transition in a single $^{171}\text{Yb}^+$ ion *IEEE Trans. Ultrason. Ferroelectr. Freq. Control* **57** 592–9

[25] Tamm C, Huntemann N, Lipphardt B, Gerginov V, Nemitz N, Kazda M, Weyers S and Peik E 2014 Cs-based optical
<table><caption>Table B1. (Continued.)</caption><thead><tr><th>Clock transitions</th><th>Atomic species</th><th>Frequency ratio</th><th>Fractional uncertainty</th></tr></thead><tbody><tr><td>ν<sub>8</sub>/ν<sub>13</sub></td><td><sup>171</sup>Yb/<sup>40</sup>Ca<sup>+</sup></td><td>1.260 931 177 231 8993(22)</td><td>1.8 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>8</sub>/ν<sub>14</sub></td><td><sup>171</sup>Yb/<sup>87</sup>Rb</td><td>75 833.197 545 114 200(25)</td><td>3.3 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>10</sub>/ν<sub>11</sub></td><td><sup>88</sup>Sr<sup>+</sup>/<sup>88</sup>Sr</td><td>1.036 230 104 446 0007(14)</td><td>1.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>10</sub>/ν<sub>12</sub></td><td><sup>88</sup>Sr<sup>+</sup>/<sup>87</sup>Sr</td><td>1.036 230 254 578 8345(14)</td><td>1.3 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>10</sub>/ν<sub>13</sub></td><td><sup>88</sup>Sr<sup>+</sup>/<sup>40</sup>Ca<sup>+</sup></td><td>1.082 076 536 381 8990(24)</td><td>2.2 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>10</sub>/ν<sub>14</sub></td><td><sup>88</sup>Sr<sup>+</sup>/<sup>87</sup>Rb</td><td>65 076.766 459 625 929(88)</td><td>1.4 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>11</sub>/ν<sub>12</sub></td><td><sup>88</sup>Sr/<sup>87</sup>Sr</td><td>1.000 000 144 883 682 799(36)</td><td>3.6 × 10<sup>-17</sup></td></tr><tr><td>ν<sub>11</sub>/ν<sub>13</sub></td><td><sup>88</sup>Sr/<sup>40</sup>Ca<sup>+</sup></td><td>1.044 243 485 823 4592(18)</td><td>1.8 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>11</sub>/ν<sub>14</sub></td><td><sup>88</sup>Sr/<sup>87</sup>Rb</td><td>62 801.462 899 418 361(21)</td><td>3.3 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>12</sub>/ν<sub>13</sub></td><td><sup>87</sup>Sr/<sup>40</sup>Ca<sup>+</sup></td><td>1.044 243 334 529 6392(18)</td><td>1.8 × 10<sup>-15</sup></td></tr><tr><td>ν<sub>12</sub>/ν<sub>14</sub></td><td><sup>87</sup>Sr/<sup>87</sup>Rb</td><td>62 801.453 800 512 449(21)</td><td>3.3 × 10<sup>-16</sup></td></tr><tr><td>ν<sub>13</sub>/ν<sub>14</sub></td><td><sup>40</sup>Ca<sup>+</sup>/<sup>87</sup>Rb</td><td>60 140.631 712 818 40(11)</td><td>1.8 × 10<sup>-15</sup></td></tr></tbody></table>

ORCID iDs

H S Margolis https://orcid.org/0000-0002-8991-3855

G Petit https://orcid.org/0000-0002-6837-3052

C Oates https://orcid.org/0000-0001-7842-8259

T Ido https://orcid.org/0000-0003-3500-6042

S Bize https://orcid.org/0000-0003-2483-5152

References

[1] Riehle F, Gill P, Arias F and Robertsson L 2018 The CIPM list of recommended frequency standard values: guidelines and procedures *Metrologia* **55** 188–200

[2] Terms of reference for the CCL-CCTF Working Group on Frequency Standards (WGFS) (available at: www.bipm.org/en/committees/cc/cctf/wg/ccl-cctf-wgfs)

[3] Consultative Committee for Time and Frequency 2021 Recommendation CCTF PSFS 2 (2021): updates to the CIPM list of standard frequencies (available at: www.bipm.org/en/committees/cc/cctf/22_2-2021)

[4] BIPM 2021 Recommended values of standard frequencies (available at: www.bipm.org/en/publications/mises-en-pratique/standard-frequencies.html)

[5] Petit G, Arias F and Panfilo G 2015 International atomic time: status and future challenges *C. R. Physique* **16** 480–8

[6] Panfilo G and Arias F 2019 The Coordinated universal Time (UTC) *Metrologia* **56** 042001

[7] Primary and Secondary Frequency Standards participating to TAI (available at: https://webtai.bipm.org/ftp/pub/tai/data/PSFS_reports/)

[8] Margolis H S and Gill P 2015 Least-squares analysis of clock frequency comparison data to deduce optimized frequency and frequency ratio values *Metrologia* **52** 628–34

[9] Robertsson L 2016 On the evaluation of ultra-high-precision frequency ratio measurements: examining closed loops in a graph theory framework *Metrologia* **53** 1272–80

[10] Margolis H S and Gill P 2016 Determination of optimized frequency and frequency ratio values from over-determined sets of clock comparison data *J. Phys.: Conf. Ser.* **723** 012060

[11] Mohr P J and Taylor B N 2000 CODATA recommended values of the fundamental physical constants: 1998 *Rev. Mod. Phys.* **72** 351–495

[12] von Zanthier J et al 2000 Absolute frequency measurement of the $\text{In}^+$ clock transition with a mode-locked laser *Opt. Lett.* **25** 1729–31

[13] Wang Y H, Dumke R, Liu T, Stejskal A, Zhao Y N, Zhang J, Lu Z H, Wang L J, Becker T and Walther H 2007 Absolute frequency measurement and high resolution spectroscopy of $^{115}\text{In}^+$ $5\text{s}^2 \text{1}\text{S}_0-5\text{s}5\text{p} \text{3}\text{P}_0$ narrowline transition *Opt. Commun.* **273** 526–31

[14] Ohtsubo N, Li Y, Matsubara K, Ido T and Hayasaka K 2017 Frequency measurement of the clock transition of an indium ion sympathetically-cooled in a linear trap *Opt. Express* **25** 11725–35

[15] Parthey C G et al 2011 Improved measurement of the hydrogen 1S–2S transition frequency *Phys. Rev. Lett.* **107** 203001

[16] Matveev A et al 2013 Precision measurement of the hydrogen 1S–2S frequency via a 920 km fiber link *Phys. Rev. Lett.* **110** 230801

[17] McFerran J J, Yi L, Mejri S, Di Manno S, Zhang W, Guéna J, Le Coq Y and Bize S 2012 Neutral atom frequency reference in the deep ultraviolet with fractional uncertainty = $5.7 \times 10^{-15}$ *Phys. Rev. Lett.* **108** 183004

[18] McFerran J J, Yi L, Mejri S, Di Manno S, Zhang W, Guéna J, Le Coq Y and Bize S 2015 Erratum: Neutral atom frequency reference in the deep ultraviolet with fractional uncertainty = $5.7 \times 10^{-15}$ [Phys. Rev. Lett. 108, 183004 (2012)] *Phys. Rev. Lett.* **115** 219901

[19] Tyumenev R et al 2016 Comparing a mercury optical lattice clock with microwave and optical frequency standards *New J. Phys.* **18** 113002

[20] Rosenband T et al 2007 Observation of the $^{1}\text{S}_0 \rightarrow ^3\text{P}_0$ clock transition in $^{27}\text{Al}^+$ *Phys. Rev. Lett.* **98** 220801

[21] Stalnaker J E et al 2007 Optical-to-microwave frequency comparison with fractional uncertainty of $10^{-15}$ *Appl. Phys. B* **89** 167–76

[22] Consultative Committee for Length 2005 *Report of the 12th Meeting, Consultative Committee for Length (CCL) (15–16 September 2005)* (available at: www.bipm.org/documents/20126/31697125/12th+meeting/058b3c8a-8914-18c1-3fe1-2e601dcbdfad)

[23] Tamm C, Weyers S, Lipphardt B and Peik E 2009 Stray-field-induced quadrupole shift and absolute frequency of the 688-THz $^{171}\text{Yb}^+$ single-ion optical frequency standard *Phys. Rev. A* **80** 043403

[24] Webster S, Godun R, King S, Huang G, Walton B, Tsatourian V, Margolis H, Lea S and Gill P 2010 Frequency measurement of the $^{2}\text{S}_{1/2} \rightarrow ^2\text{D}_{3/2}$ electric quadrupole transition in a single $^{171}\text{Yb}^+$ ion *IEEE Trans. Ultrason. Ferroelectr. Freq. Control* **57** 592–9

[25] Tamm C, Huntemann N, Lipphardt B, Gerginov V, Nemitz N, Kazda M, Weyers S and Peik E 2014 Cs-based optical
frequency measurement using cross-linked optical and
microwave oscillators *Phys. Rev.* A **89** 023820

[26] Godun R M, Nisbet-Jones P B R, Jones J M, King S A, Johnson L A M, Margolis H S, Szymaniec K, Lea S N, Bongs K and Gill P 2014 Frequency ratio of two optical clock transitions in $^{171}$Yb$^+$ and constraints on the time variation of fundamental constants *Phys. Rev. Lett.* **113** 210801

[27] Hosaka K, Webster S A, Stannard A, Walton B R, Margolis H S and Gill P 2009 Frequency measurement of the $ ^2S_{1/2} - ^2F_{7/2} $ electric octupole transition in a single $ ^{171}\text{Yb}^+ $ ion *Phys. Rev. A* **79** 033403

[28] Huntemann N, Okhapkin M, Lipphardt B, Weyers S, Tamm C and Peik E 2012 High-accuracy optical clock based on the octupole transition in $ ^{171}\text{Yb}^+ $ *Phys. Rev. Lett.* **108** 090801

[29] King S A, Godun R M, Webster S A, Margolis H S, Johnson L A M, Szymaniec K, Baird P E G and Gill P 2012 Absolute frequency measurement of the $ ^2S_{1/2} - ^2F_{7/2} $ electric octupole transition in a single ion of $ ^{171}\text{Yb}^+ $ with $10^{-15}$ fractional uncertainty *New J. Phys.* **14** 013045

[30] Huntemann N, Lipphardt B, Tamm C, Gerginov V, Weyers S and Peik E 2014 Improved limit on a temporal variation of $m_p/m_e$ from comparisons of Yb$^+$ and Cs atomic clocks *Phys. Rev. Lett.* **113** 210802

[31] Kohno T, Yasuda M, Hosaka K, Inaba H, Nakajima Y and Hong F-L 2009 One-dimensional optical lattice clock with a fermionic $^{171}$Yb isotope *Appl. Phys. Express* **2** 072501

[32] Yasuda M *et al* 2012 Improved absolute frequency measurement of the $ ^{171}\text{Yb} $ optical lattice clock towards a candidate for the redefinition of the second *Appl. Phys. Express* **5** 102401

[33] Lemke N D, Ludlow A D, Barber Z W, Fortier T M, Diddams S A, Jiang Y, Jefferts S R, Heavner T P, Parker T E and Oates C W 2009 Spin-1/2 optical lattice clock *Phys. Rev. Lett.* **103** 063001

[34] Park C Y *et al* 2013 Absolute frequency measurement of $ ^1S_0 $ ($F=1/2 \rightarrow ^3P_0$ ($F=1/2$)) transition of $ ^{171}\text{Yb} $ atoms in a one-dimensional optical lattice at KRISS *Metrologia* **50** 119-28

[35] Pizzocaro M, Thoumany P, Rauf B, Bregolin F, Milani G, Clivati C, Costanzo G A, Levi F and Calonico D 2017 Absolute frequency measurement of the $ ^1S_0 - ^3P_0 $ transition of $ ^{171}\text{Yb} $ *Metrologia* **54** 102

[36] Kim H, Heo M-S, Lee W-K, Park C Y, Hong H-G, Hwang S-W and Yu D-H 2017 Improved absolute frequency measurement of the $ ^{171}\text{Yb} $ optical lattice clock at KRISS relative to the SI second *Jpn. J. Appl. Phys.* **56** 050302

[37] Degenhardt C *et al* 2005 Calcium optical frequency standard with ultracold atoms: Approaching $10^{-15}$ relative uncertainty *Phys. Rev. A* **72** 062111

[38] Wilpers G, Oates C W and Hollberg L 2006 Improved uncertainty budget for optical frequency measurements with microkelvin neutral atoms: results for a high-stability $ ^{40}\text{Ca} $ optical frequency standard *Appl. Phys. B* **85** 31-44

[39] Wilpers G *et al* 2007 Absolute frequency measurement of the neutral $ ^{40}\text{Ca} $ optical frequency standard at 657 nm based on microkelvin atoms *Metrologia* **44** 146-51

[40] Margolis H S, Barwood G P, Huang G, Klein H A, Lea S N, Szymaniec K and Gill P 2004 Hertz-level measurement of the optical clock frequency in a single $ ^{88}\text{Sr}^+ $ ion *Science* **306** 1355-8

[41] Dubé P, Madej A A, Bernard J E, Marmet L, Boulanger J-S and Cundy S 2005 Electric quadrupole shift cancellation in single-ion optical frequency standards *Phys. Rev. Lett.* **95** 033001

[42] Madej A A, Dubé P, Zhou Z, Bernard J E and Gertsvolf M 2012 $ ^{88}\text{Sr}^+ $ 445-THz single-ion reference at the $10^{-17}$ level via control and cancellation of systematic uncertainties and its measurement against the SI second *Phys. Rev. Lett.* **109** 203002

[43] Barwood G P, Huang G, Klein H A, Johnson L A M, King S A, Margolis H S, Szymaniec K and Gill P 2014 Agreement between two $ ^{88}\text{Sr}^+ $ optical clocks to 4 parts in $10^{-17}$ *Phys. Rev. A* **89** 050501

[44] Dubé P, Bernard J E and Gertsvolf M 2017 Absolute frequency measurement of the $ ^{88}\text{Sr}^+ $ clock transition using a GPS link to the SI second *Metrologia* **54** 290-8

[45] Baillard X, Fouché M, Le Targat R, Westergaard P G, Lecallier A, Le Coq Y, Rovera G D, Bize S and Lemonde P 2007 Accuracy evaluation of an optical lattice clock with bosonic atoms *Opt. Lett.* **32** 1812-4

[46] Morzyński P *et al* 2015 Absolute measurement of the $ ^1S_0 - ^3P_0 $ clock transition in neutral $ ^{88}\text{Sr} $ over the 330 km-long stabilized fibre optic link *Sci. Rep.* **5** 17495

[47] Boyd M M, Ludlow A D, Blatt S, Foreman S M, Ido T, Zelevinsky T and Ye J 2007 $ ^{87}\text{Sr} $ lattice clock with inaccuracy below $10^{-15}$ *Phys. Rev. Lett.* **98** 083002

[48] Campbell G K *et al* 2008 The absolute frequency of the $ ^{87}\text{Sr} $ optical clock transition *Metrologia* **45** 539-48

[49] Baillard X *et al* 2008 An optical lattice clock with spin-polarized $ ^{87}\text{Sr} $ atoms *Eur. Phys. J. D* **48** 11-17

[50] Falke S *et al* 2011 The $ ^{87}\text{Sr} $ optical frequency standard at PTB *Metrologia* **48** 399

[51] Yamaguchi A, Shiga N, Nagano S, Li Y, Ishijima H Hachisu H, Kumagai M and Ido T 2012 Stability transfer between two clock lasers operating at different wavelengths for absolute frequency measurement of clock transition in $ ^{87}\text{Sr} $ *Appl. Phys. Express* **5** 022701

[52] Akamatsu D, Inaba H, Hosaka K, Yasuda M, Onae A, Suzuyama T, Amemiya M and Hong F-L 2014 Spectroscopy and frequency measurement of the $ ^{87}\text{Sr} $ clock transition by laser linewidth transfer using an optical frequency comb *Appl. Phys. Express* **7** 012401

[53] Tanabe T *et al* 2015 Improved frequency measurement of the $ ^1S_0 - ^3P_0 $ clock transition in $ ^{87}\text{Sr} $ using a Cs fountain clock as a transfer oscillator *J. Phys. Soc. Japan* **84** 115002

[54] Lin Y-G, Wang Q, Li Y, Meng F, Lin B-K, Zang E-J, Sun Z, Fang F, Li T-C and Fang Z-J 2015 First evaluation and frequency measurement of the strontium optical lattice clock at NIM *Chin. Phys. Lett.* **32** 090601

[55] Falke S *et al* 2014 A strontium lattice clock with $3 \times 10^{-17}$ inaccuracy and its frequency *New J. Phys.* **16** 073023

[56] Le Targat R *et al* 2013 Experimental realization of an optical second with strontium lattice clocks *Nat. Commun.* **4** 2109

[57] Lodewyck J *et al* 2016 Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock *Metrologia* **53** 1123

[58] Grebing C, Al-Masoudi A, Dörscher S, Häfner S, Gerginov V, Weyers S, Lipphardt B, Riehle F, Sterr U and Lisdat C 2016 Realization of a timescale with an accurate optical lattice clock *Optica* **3** 563-9

[59] Hachisu H, Petit G and Ido T 2017 Absolute frequency measurement with uncertainty below $1 \times 10^{-15}$ using international atomic time *Appl. Phys. B* **123** 34

[60] Hachisu H, Petit G, Nakagawa F, Hanado Y and Ido T 2017 SI-traceable measurement of an optical frequency at the low $10^{-16}$ level without a local primary standard *Opt. Express* **25** 8511-23

[61] Chwalla M *et al* 2009 Absolute frequency measurement of the $ ^{40}\text{Ca} $ $4\text{s} \ ^2S_{1/2} - 3\text{d} \ ^2D_{5/2} $ clock transition *Phys. Rev. Lett.* **102** 023002
frequency measurement using cross-linked optical and
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[26] Godun R M, Nisbet-Jones P B R, Jones J M, King S A, Johnson L A M, Margolis H S, Szymaniec K, Lea S N, Bongs K and Gill P 2014 Frequency ratio of two optical clock transitions in $^{171}$Yb$^+$ and constraints on the time variation of fundamental constants *Phys. Rev. Lett.* **113** 210801

[27] Hosaka K, Webster S A, Stannard A, Walton B R, Margolis H S and Gill P 2009 Frequency measurement of the $ ^2S_{1/2} - ^2F_{7/2} $ electric octupole transition in a single $ ^{171}\text{Yb}^+ $ ion *Phys. Rev. A* **79** 033403

[28] Huntemann N, Okhapkin M, Lipphardt B, Weyers S, Tamm C and Peik E 2012 High-accuracy optical clock based on the octupole transition in $ ^{171}\text{Yb}^+ $ *Phys. Rev. Lett.* **108** 090801

[29] King S A, Godun R M, Webster S A, Margolis H S, Johnson L A M, Szymaniec K, Baird P E G and Gill P 2012 Absolute frequency measurement of the $ ^2S_{1/2} - ^2F_{7/2} $ electric octupole transition in a single ion of $ ^{171}\text{Yb}^+ $ with $ 10^{-15} $ fractional uncertainty *New J. Phys.* **14** 013045

[30] Huntemann N, Lipphardt B, Tamm C, Gerginov V, Weyers S and Peik E 2014 Improved limit on a temporal variation of $m_p/m_e$ from comparisons of Yb$^+$ and Cs atomic clocks *Phys. Rev. Lett.* **113** 210802

[31] Kohno T, Yasuda M, Hosaka K, Inaba H, Nakajima Y and Hong F-L 2009 One-dimensional optical lattice clock with a fermionic $ ^{171}\text{Yb} $ isotope *Appl. Phys. Express* **2** 072501

[32] Yasuda M et al 2012 Improved absolute frequency measurement of the $ ^{171}\text{Yb} $ optical lattice clock towards a candidate for the redefinition of the second *Appl. Phys. Express* **5** 102401

[33] Lemke N D, Ludlow A D, Barber Z W, Fortier T M, Diddams S A, Jiang Y, Jefferts S R, Heavner T P, Parker T E and Oates C W 2009 Spin-1/2 optical lattice clock *Phys. Rev. Lett.* **103** 063001

[34] Park C Y et al 2013 Absolute frequency measurement of $ ^1S_0 $ ($F=1/2 \rightarrow ^3P_0$ ($F=1/2$)) transition of $ ^{171}\text{Yb} $ atoms in a one-dimensional optical lattice at KRISS Metrologia **50** 119-28

[35] Pizzocaro M, Thoumany P, Rauf B, Bregolin F, Milani G, Clivati C, Costanzo G A, Levi F and Calonico D 2017 Absolute frequency measurement of the $ ^1S_0 - ^3P_0 $ transition of $ ^{171}\text{Yb} $ Metrologia **54** 102

[36] Kim H, Heo M-S, Lee W-K, Park C Y, Hong H-G, Hwang S-W and Yu D-H 2017 Improved absolute frequency measurement of the $ ^{171}\text{Yb} $ optical lattice clock at KRISS relative to the SI second *Jpn. J. Appl. Phys.* **56** 050302

[37] Degenhardt C et al 2005 Calcium optical frequency standard with ultracold atoms: Approaching $10^{-15}$ relative uncertainty *Phys. Rev. A* **72** 062111

[38] Wilpers G, Oates C W and Hollberg L 2006 Improved uncertainty budget for optical frequency measurements with microkelvin neutral atoms: results for a high-stability $ ^{40}\text{Ca} $ optical frequency standard *Appl. Phys. B* **85** 31-44

[39] Wilpers G et al 2007 Absolute frequency measurement of the neutral $ ^{40}\text{Ca} $ optical frequency standard at 657 nm based on microkelvin atoms *Metrologia* **44** 146-51

[40] Margolis H S, Barwood G P, Huang G, Klein H A, Lea S N, Szymaniec K and Gill P 2004 Hertz-level measurement of the optical clock frequency in a single $ ^{88}\text{Sr}^+ $ ion *Science* **306** 1355-8

[41] Dubé P, Madej A A, Bernard J E, Marmet L, Boulanger J-S and Cundy S 2005 Electric quadrupole shift cancellation in single-ion optical frequency standards *Phys. Rev. Lett.* **95** 033001

[42] Madej A A, Dubé P, Zhou Z, Bernard J E and Gertsvolf M 2012 $ ^{88}\text{Sr}^+ $ 445-THz single-ion reference at the $ 10^{-17} $ level via control and cancellation of systematic uncertainties and its measurement against the SI second *Phys. Rev. Lett.* **109** 203002

[43] Barwood G P, Huang G, Klein H A, Johnson L A M, King S A, Margolis H S, Szymaniec K and Gill P 2014 Agreement between two $ ^{88}\text{Sr}^+ $ optical clocks to 4 parts in $ 10^{17} $ *Phys. Rev. A* **89** 050501

[44] Dubé P, Bernard J E and Gertsvolf M 2017 Absolute frequency measurement of the $ ^{88}\text{Sr}^+ $ clock transition using a GPS link to the SI second *Metrologia* **54** 290-8

[45] Baillard X, Fouché M, Le Targat R, Westergaard P G, Lecallier A, Le Coq Y, Rovera G D, Bize S and Lemonde P 2007 Accuracy evaluation of an optical lattice clock with bosonic atoms *Opt. Lett.* **32** 1812-4

[46] Morzyński P et al 2015 Absolute measurement of the $ ^1S_0 - ^3P_0 $ clock transition in neutral $ ^{88}\text{Sr} $ over the 330 km-long stabilized fibre optic link *Sci. Rep.* **5** 17495

[47] Boyd M M, Ludlow A D, Blatt S, Foreman S M, Ido T, Zelevinsky T and Ye J 2007 $ ^{87}\text{Sr} $ lattice clock with inaccuracy below $ 10^{-15} $ *Phys. Rev. Lett.* **98** 083002

[48] Campbell G K et al 2008 The absolute frequency of the $ ^{87}\text{Sr} $ optical clock transition *Metrologia* **45** 539-48

[49] Baillard X et al 2008 An optical lattice clock with spin-polarized $ ^{87}\text{Sr} $ atoms *Eur. Phys. J. D* **48** 11-17

[50] Falke S et al 2011 The $ ^{87}\text{Sr} $ optical frequency standard at PTB *Metrologia* **48** 399

[51] Yamaguchi A, Shiga N, Nagano S, Li Y, Ishijima H Hachisu H, Kumagai M and Ido T 2012 Stability transfer between two clock lasers operating at different wavelengths for absolute frequency measurement of clock transition in $ ^{87}\text{Sr} $ *Appl. Phys. Express* **5** 022701

[52] Akamatsu D, Inaba H, Hosaka K, Yasuda M, Onae A, Suzuyama T, Amemiya M and Hong F-L 2014 Spectroscopy and frequency measurement of the $ ^{87}\text{Sr} $ clock transition by laser linewidth transfer using an optical frequency comb *Appl. Phys. Express* **7** 012401

[53] Tanabe T et al 2015 Improved frequency measurement of the $ ^1S_0 - ^3P_0 $ clock transition in $ ^{87}\text{Sr} $ using a Cs fountain clock as a transfer oscillator *J. Phys. Soc. Japan* **84** 115002

[54] Lin Y-G, Wang Q, Li Y, Meng F, Lin B-K, Zang E-J, Sun Z, Fang F, Li T-C and Fang Z-J 2015 First evaluation and frequency measurement of the strontium optical lattice clock at NIM *Chin. Phys. Lett.* **32** 090601

[55] Falke S et al 2014 A strontium lattice clock with $3 \times 10^{-17}$ inaccuracy and its frequency *New J. Phys.* **16** 073023

[56] Le Targat R et al 2013 Experimental realization of an optical second with strontium lattice clocks *Nat. Commun.* **4** 2109

[57] Lodewyck J et al 2016 Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock *Metrologia* **53** 1123

[58] Grebing C, Al-Masoudi A, Dörscher S, Häfner S, Gerginov V, Weyers S, Lipphardt B, Riehle F, Sterr U and Lisdat C 2016 Realization of a timescale with an accurate optical lattice clock *Optica* **3** 563-9

[59] Hachisu H, Petit G and Ido T 2017 Absolute frequency measurement with uncertainty below $1 \times 10^{-15}$ using international atomic time *Appl. Phys. B* **123** 34

[60] Hachisu H, Petit G, Nakagawa F, Hanado Y and Ido T 2017 SI-traceable measurement of an optical frequency at the low $10^{-16}$ level without a local primary standard *Opt. Express* **25** 8511-23

[61] Chwalla M et al 2009 Absolute frequency measurement of the $ ^{40}\text{Ca} $ $ 4s $ $ ^2S_{1/2} - 3d $ $ ^2D_{5/2} $ clock transition *Phys. Rev. Lett.* **102** 023002
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[63] Huang Y, Guan H, Liu P, Bian W, Ma L, Liang K, Li T and Gao K 2016 Frequency comparison of two $^{40}$Ca$^+$ optical clocks with an uncertainty at the $10^{-17}$ level *Phys. Rev. Lett.* **116** 013001

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[66] Guéna J et al 2017 First international comparison of fountain primary frequency standards via a long distance optical fiber link *Metrologia* **54** 348–54

[67] Wang Y H, Liu T, Dumke R, Stejskal A, Zhao Y N, Zhang J, Lu Z H, Wang L J, Becker T and Walther H 2007 Improved absolute frequency measurement of the $^{115}$In$^+$ 5s$^2$ $^1$S$_0$–5s5p $^3$P$_0$ narrowline transition: progress towards an optical frequency standard *Laser Phys.* **17** 1017–24

[68] Yamanaka K, Ohmae N, Ushijima I, Takamoto M and Katori H 2015 Frequency ratio of $^{199}$Hg and $^{87}$Sr optical lattice clocks beyond the SI limit *Phys. Rev. Lett.* **114** 230801

[69] Rosenband T et al 2008 Frequency ratio of $Al^+$ and $Hg^+$ single-ion optical clocks; metrology at the 17th decimal place *Science* **319** 1808–12

[70] Akamatsu D, Yasuda M, Inaba H, Hosaka K, Tanabe T, Onae A and Hong F-L 2014 Frequency ratio measurement of $^{171}$Yb and $^{87}$Sr optical lattice clocks *Opt. Express* **22** 7898–905

[71] Akamatsu D, Yasuda M, Inaba H, Hosaka K, Tanabe T, Onae A and Hong F-L 2014 Errata: Frequency ratio measurement of $^{171}$Yb and $^{87}$Sr optical lattice clocks *Opt. Express* **22** 32199

[72] Takamoto M et al 2015 Frequency ratios of Sr, Yb and Hg based optical lattice clocks and their applications *C. R. Physique* **16** 489–98

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[74] Takano T, Mizushima R and Katori H 2017 Precise determination of the isotope shift of $^{88}$Sr–$^{87}$Sr optical lattice clock by sharing perturbations *Appl. Phys. Express* **10** 072801

[75] Ohtsubo N, Li Y, Nemitz N, Hachisu H, Matsubara K, Ido T and Hayasaka K 2020 Frequency ratio of an $^{115}$In$^+$ ion clock and a $^{87}$Sr optical lattice clock *Opt. Lett.* **45** 5950–3

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[63] Huang Y, Guan H, Liu P, Bian W, Ma L, Liang K, Li T and Gao K 2016 Frequency comparison of two $^{40}$Ca$^+$ optical clocks with an uncertainty at the $10^{-17}$ level *Phys. Rev. Lett.* **116** 013001

[64] LNE-SYRTE TAI data; MJD 55954-57867 (January 2012–April 2017) Request of the CCL-CCTF WGFS by Guéna J on 10 May 2017 (submitted)

[65] Ovchinnikov Y B, Szymaniec K and Edris S 2015 Measurement of rubidium ground-state hyperfine transition frequency using atomic fountains *Metrologia* **52** 595–9

[66] Guéna J et al 2017 First international comparison of fountain primary frequency standards via a long distance optical fiber link *Metrologia* **54** 348–54

[67] Wang Y H, Liu T, Dumke R, Stejskal A, Zhao Y N, Zhang J, Lu Z H, Wang L J, Becker T and Walther H 2007 Improved absolute frequency measurement of the $^{115}$In$^+$ 5s$^2$ $^1$S$_0$–5s5p $^3$P$_0$ narrowline transition: progress towards an optical frequency standard *Laser Phys.* **17** 1017–24

[68] Yamanaka K, Ohmae N, Ushijima I, Takamoto M and Katori H 2015 Frequency ratio of $^{199}$Hg and $^{87}$Sr optical lattice clocks beyond the SI limit *Phys. Rev. Lett.* **114** 230801

[69] Rosenband T et al 2008 Frequency ratio of $Al^+$ and $Hg^+$ single-ion optical clocks; metrology at the 17th decimal place *Science* **319** 1808–12

[70] Akamatsu D, Yasuda M, Inaba H, Hosaka K, Tanabe T, Onae A and Hong F-L 2014 Frequency ratio measurement of $^{171}$Yb and $^{87}$Sr optical lattice clocks *Opt. Express* **22** 7898–905

[71] Akamatsu D, Yasuda M, Inaba H, Hosaka K, Tanabe T, Onae A and Hong F-L 2014 Errata: Frequency ratio measurement of $^{171}$Yb and $^{87}$Sr optical lattice clocks *Opt. Express* **22** 32199

[72] Takamoto M et al 2015 Frequency ratios of Sr, Yb and Hg based optical lattice clocks and their applications *C. R. Physique* **16** 489–98

[73] Nemitz N, Ohkubo T, Takamoto M, Ushijima I, Das M, Ohmae N and Katori H 2016 Frequency ratio of Yb and Sr clocks with $5 \times 10^{-17}$ uncertainty at 150 seconds averaging time *Nat. Photon.* **10** 258–61

[74] Takano T, Mizushima R and Katori H 2017 Precise determination of the isotope shift of $^{88}$Sr–$^{87}$Sr optical lattice clock by sharing perturbations *Appl. Phys. Express* **10** 072801

[75] Ohtsubo N, Li Y, Nemitz N, Hachisu H, Matsubara K, Ido T and Hayasaka K 2020 Frequency ratio of an $^{115}$In$^+$ ion clock and a $^{87}$Sr optical lattice clock *Opt. Lett.* **45** 5950–3

[76] Leopardi H et al 2021 Measurement of the $^{27}$Al$^+$ and $^{87}$Sr absolute optical frequencies *Metrologia* **58** 015017

[77] Baynham C F A et al 2018 Absolute frequency measurement of the $^2S_{1/2}$–$^2F_{7/2}$ optical clock transition in $^{171}$Yb$^+$ with an uncertainty of $4 \times 10^{-16}$ using a frequency link to International Atomic Time *J. Mod. Opt.* **65** 585–91

[78] Lange R, Huntemann N, Rahm J M, Sanner C, Shao H, Lipphardt B, Tamm C, Weyers S and Peik E 2021 Improved limits for violations of local position invariance from atomic clock comparisons *Phys. Rev. Lett.* **126** 011102

[79] Luo L et al 2020 Absolute frequency measurement of an Yb optical clock at the $10^{-16}$ level using International Atomic Time *Metrologia* **57** 065017

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