Yb/Sr clock frequency measurement toward the redefinition of the second

1. BIPM, The International System of Units (2009).

2. S. Weyers, V. Gerginov, M. Kazda, J. Rahm, B. Lipphardt, G. Dobrev, and K. Gibble, "Advances in the accuracy, stability, and reliability of the PTB primary fountain clocks," Metrologia 55, 789–805 (2018).

3. S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "A microfabricated atomic clock," Appl. Phys. Lett. 85, 1460–1462 (2004).

4. Y. Ovchinnikov and G. Marra, "Accurate rubidium atomic fountain frequency standard," Metrologia 48, 87–100 (2011).

5. S. Knappe, P. D. D. Schwindt, V. Shah, L. Hollberg, J. Kitching, L. Liew, and J. Moreland, "A chip-scale atomic clock based on 87Rb with improved frequency stability," Opt. Express 13, 1249–1253 (2005).

6. H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, and G. Zinner, "Phase coherent frequency measurement of visible radiation," Phys. Rev. Lett. 76, 18–21 (1996).

7. H. S. Margolis, G. P. Barwood, G. Huang, H. A. Klein, S. N. Lea, K. Szymaniec, and P. Gill, "Hertz-level measurement of the optical clock frequency in a single 88Sr+ ion," Science 306, 1355–1358 (2004).

8. M. Takamoto, F.-L. Hong, R. Higashi, and H. Katori, "An optical lattice clock.," Nature 435, 321–324 (2005).

9. U. Sterr, C. Degenhardt, H. Stoehr, C. Lisdat, H. Schnatz, J. Helmcke, F. Riehle, G. Wilpers, C. Oates, and L. Hollberg, "The optical calcium frequency standards of PTB and NIST," Comptes Rendus Phys. 5, 845–855 (2004).

10. H. Katori, M. Takamoto, V. G. Pal’chikov, and V. D. Ovsiannikov, "Ultrastable optical clock with neutral atoms in an engineered light shift trap.," Phys. Rev. Lett. 91, 173005 (2003).

11. I. Ushijima, M. Takamoto, M. Das, T. Ohkubo, and H. Katori, "Cryogenic optical lattice clocks," Nat. Photonics 9, 185–189 (2015).

12. T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, "Systematic evaluation of an atomic clock at 2 × 10－18 total uncertainty," Nat. Commun. 6, 6896 (2015).

13. W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schäffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, "Atomic clock performance enabling geodesy below the centimetre level," Nature 564, 87–90 (2018).

14. S. M. Brewer, J. S. Chen, A. M. Hankin, E. R. Clements, C. W. Chou, D. J. Wineland, D. B. Hume, and D. R. Leibrandt, "Al+ 27 Quantum-Logic Clock with a Systematic Uncertainty below 10-18," Phys. Rev. Lett. 123, 033201 (2019).

15. T. Bothwell, D. Kedar, E. Oelker, J. M. Robinson, S. L. Bromley, W. L. Tew, J. Ye, and C. J. Kennedy, "JILA SrI optical lattice clock with uncertainty of 2.0 × 10－18," Metrologia 56, 065004 (2019).

16. C. Sanner, N. Huntemann, R. Lange, C. Tamm, E. Peik, M. S. Safronova, and S. G. Porsev, "Optical clock comparison for Lorentz symmetry testing," Nature 567, 204–208 (2019).

17. M. Takamoto, I. Ushijima, N. Ohmae, T. Yahagi, K. Kokado, H. Shinkai, and H. Katori, "Test of general relativity by a pair of transportable optical lattice clocks," Nat. Photonics 14, 411–415 (2020).

18. G. Lion, I. Panet, P. Wolf, C. Guerlin, S. Bize, and P. Delva, "Determination of a high spatial resolution geopotential model using atomic clock comparisons," J. Geod. 91, 597–611 (2017).

19. T. Takano, M. Takamoto, I. Ushijima, N. Ohmae, T. Akatsuka, A. Yamaguchi, Y. Kuroishi, H. Munekane, B. Miyahara, and H. Katori, "Geopotential measurements with synchronously linked optical lattice clocks," Nat. Photonics 10, 662–666 (2016).

20. R. Bondarescu, A. Schärer, A. Lundgren, G. Hetényi, N. Houlié, P. Jetzer, and M. Bondarescu, "Ground-based optical atomic clocks as a tool to monitor vertical surface motion," Geophys. J. Int. 202, 1770–1774 (2015).

21. N. Huntemann, B. Lipphardt, C. Tamm, V. Gerginov, S. Weyers, and E. Peik, "Improved limit on a temporal variation of mp/me from comparisons of Yb+ and Cs atomic clocks," Phys. Rev. Lett. 113, 210802 (2014).

22. P. Wcisło, P. Morzyński, M. Bober, A. Cygan, D. Lisak, R. Ciuryło, and M. Zawada, "Experimental constraint on dark matter detection with optical atomic clocks," Nat. Astron. 1, 0009 (2016).

23. P. Wcisło, P. Ablewski, K. Beloy, S. Bilicki, M. Bober, R. Brown, R. Fasano, R. Ciuryło, H. Hachisu, T. Ido, J. Lodewyck, A. Ludlow, W. McGrew, P. Morzyński, D. Nicolodi, M. Schioppo, M. Sekido, R. Le Targat, P. Wolf, X. Zhang, B. Zjawin, and M. Zawada, "New bounds on dark matter coupling from a global network of optical atomic clocks," Sci. Adv. 4, eaau4869 (2018).

24. S. Kolkowitz, I. Pikovski, N. Langellier, M. D. Lukin, R. L. Walsworth, and J. Ye, "Gravitational wave detection with optical lattice atomic clocks," Phys. Rev. D 94, 124043 (2016).

25. S. B. Koller, J. Grotti, S. Vogt, A. Al-Masoudi, S. Dörscher, S. Häfner, U. Sterr, and C. Lisdat, "Transportable Optical Lattice Clock with 7×10-17 Uncertainty," Phys. Rev. Lett. 118, 073601 (2017).

26. T. Kobayashi, D. Akamatsu, K. Hosaka, Y. Hisai, M. Wada, H. Inaba, T. Suzuyama, F. Hong, and M. Yasuda, "Demonstration of the nearly continuous operation of an 171Yb optical lattice clock for half a year," Metrologia 57, 065021 (2020).

27. D. Świerad, S. Häfner, S. Vogt, B. Venon, D. Holleville, S. Bize, A. Kulosa, S. Bode, Y. Singh, K. Bongs, E. M. Rasel, J. Lodewyck, R. Le Targat, C. Lisdat, and U. Sterr, "Ultra-stable clock laser system development towards space applications," Sci. Rep. 6, 33973 (2016).

28. S. Origlia, M. S. Pramod, and S. Schiller, "Towards an optical clock for space: Compact, high-performance optical lattice clock based on bosonic atoms," Phys. Rev. A 98, 053443 (2018).

29. I. Courtillot, A. Quessada-Vial, A. Brusch, D. Kolker, G. D. Rovera, and P. Lemonde, "Accurate spectroscopy of Sr atoms," Eur. Phys. J. D 33, 161–171 (2005).

30. S.-Y. Lan, P.-C. Kuan, B. Estey, D. English, J. M. Brown, M. A. Hohensee, and H. Müller, "A Clock Directly Linking Time to a Particle’s Mass," Science 339, 554–557 (2013).

31. F. Riehle, P. Gill, F. Arias, and L. Robertsson, "The CIPM list of recommended frequency standard values: guidelines and procedures," Metrologia 55, 188–200 (2018).

32. T. Kohno, M. Yasuda, K. Hosaka, H. Inaba, Y. Nakajima, and F.-L. Hong, "Onedimensional optical lattice clock with a fermionic 171Yb isotope," Appl. Phys. Express 2, 072501 (2009).

33. D. Akamatsu, H. Inaba, K. Hosaka, M. Yasuda, A. Onae, T. Suzuyama, M. Amemiya, and F.-L. Hong, "Spectroscopy and frequency measurement of the 87Sr clock transition by laser linewidth transfer using an optical frequency comb," Appl. Phys. Express 7, 012401 (2014).

34. D. Akamatsu, M. Yasuda, H. Inaba, K. Hosaka, T. Tanabe, A. Onae, and F.-L. Hong, "Frequency ratio measurement of 171Yb and 87Sr optical lattice clocks," Opt. Express 22, 7898–7905 (2014).

35. D. Akamatsu, M. Yasuda, H. Inaba, K. Hosaka, T. Tanabe, A. Onae, and F. Hong, "Errata : Frequency ratio measurement of 171Yb and 87Sr optical lattice clocks," Opt. Express 22, 32199 (2014).

36. N. Nemitz, T. Ohkubo, M. Takamoto, I. Ushijima, M. Das, N. Ohmae, and H. Katori, "Frequency ratio of Yb and Sr clocks with 5 × 10-17 uncertainty at 150 seconds averaging time," Nat. Photonics 10, 258–261 (2016).

37. K. Yamanaka, N. Ohmae, I. Ushijima, M. Takamoto, and H. Katori, "Frequency ratio of 199Hg and 87Sr optical lattice clocks beyond the SI limit," Phys. Rev. Lett. 114, 230801 (2015).

38. B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, "An optical lattice clock with accuracy and stability at the 10-18 level," Nature 506, 71–75 (2014).

39. M. Pizzocaro, F. Bregolin, P. Barbieri, B. Rauf, F. Levi, and D. Calonico, "Absolute frequency measurement of the 1S0- 3P0 transition of 171Yb with a link to international atomic time," Metrologia 57, 035007 (2020).

40. N. Ohmae, F. Bregolin, N. Nemitz, and H. Katori, "Direct measurement of the frequency ratio for Hg and Yb optical lattice clocks and closure of the Hg/Yb/Sr loop," Opt. Express 28, 15112–15121 (2020).

41. A. Arvanitaki, J. Huang, and K. Van Tilburg, "Searching for dilaton dark matter with atomic clocks," Phys. Rev. D 91, 015015 (2015).

42. Y. Hisai, K. Ikeda, H. Sakagami, T. Horikiri, T. Kobayashi, K. Yoshii, and F.-L. Hong, "Evaluation of laser frequency offset locking using an electrical delay line," Appl. Opt. 57, 5628–5634 (2018).

43. J. J. Mcferran, "Laser stabilization with a frequency-to-voltage chip for narrowline laser cooling," Opt. Lett. 43, 1475–1478 (2018).

44. G. Ritt, G. Cennini, C. Geckeler, and M. Weitz, "Laser frequency offset locking using a side of filter technique," Appl. Phys. B 79, 363–365 (2004).

45. N. Strauß, I. Ernsting, S. Schiller, A. Wicht, P. Huke, and R. H. Rinkleff, "A simple scheme for precise relative frequency stabilization of lasers," Appl. Phys. B 88, 21–28 (2007).

46. G. Puentes, "Laser frequency offset locking scheme for high-field imaging of cold atoms," Appl. Phys. B 107, 11–16 (2012).

47. U. Schunemann, H. Engler, R. Grimm, M. Weidemuller, and M. Zielonkowski, "Simple scheme for tunable frequency offset locking of two lasers," Rev. Sci. Instrum. 70, 242–243 (1999).

48. K. Komori, Y. Takasu, M. Kumakura, Y. Takahashi, and T. Yabuzaki, "InjectionLocking of Blue Laser Diodes and Its Application to the Laser Cooling of Neutral Ytterbium Atoms," Jpn. J. Appl. Phys. 42, 5059–5062 (2003).

49. F. L. Hong, J. Ishikawa, Y. Zhang, R. Guo, A. Onae, and H. Matsumoto, "Frequency reproducibility of an iodine-stabilized Nd:YAG laser at 532 nm," Opt. Commun. 235, 377–385 (2004).

50. Y. Hisai, D. Akamatsu, T. Kobayashi, S. Okubo, H. Inaba, K. Hosaka, M. Yasuda, and F.-L. Hong, "Development of 8-branch Er:fiber frequency comb for Sr and Yb optical lattice clocks," Opt. Express 27, 6404–6414 (2019).

51. M. Yasuda, H. Inaba, T. Kohno, T. Tanabe, Y. Nakajima, and K. Hosaka, "Improved Absolute Frequency Measurement of the 171Yb Optical Lattice Clock towards the Redefinition of the Second," Appl. Phys. Express 5, 102401 (2012).

52. T. Kobayashi, D. Akamatsu, Y. Hisai, T. Tanabe, H. Inaba, T. Suzuyama, F.-L. Hong, K. Hosaka, and M. Yasuda, "Uncertainty Evaluation of an 171Yb Optical Lattice Clock at NMIJ," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 65, 2449–2458 (2018).

53. H. Leopardi, J. Davila-Rodriguez, F. Quinlan, J. Olson, J. A. Sherman, S. A. Diddams, and T. M. Fortier, "Single-branch Er:fiber frequency comb for precision optical metrology with 10－18 fractional instability," Optica 4, 879–885 (2017).

54. N. Ohmae, N. Kuse, M. E. Fermann, and H. Katori, "All-polarizationmaintaining , single-port Er : fiber comb for high- stability comparison of optical lattice clocks," Appl. Phys. Express 10, 062503 (2017).

55. H. Inaba, Y. Daimon, F.-L. Hong, A. Onae, K. Minoshima, T. R. Schibli, H. Matsumoto, M. Hirano, T. Okuno, M. Onishi, and M. Nakazawa, "Long-term measurement of optical frequencies using a simple, robust and low-noise fiber based frequency comb," Opt. Express 14, 5223–5231 (2006).

56. K. Kashiwagi, Y. Nakajima, M. Wada, S. Okubo, and H. Inaba, "Multi-branch fiber comb with relative frequency uncertainty at 10－20 using fiber noise difference cancellation," Opt. Express 26, 8831–8840 (2018).

57. H. Inaba, S. Yanagimachi, F.-L. Hong, A. Onae, Y. Koga, and H. Matsumoto, "Stability degradation factors evaluated by phase noise measurement in an optical-microwave frequency link using an optical frequency comb," IEEE Trans. Instrum. Meas. 54, 763–766 (2005).

58. D. J. Jones, S. A. Diddams, K. Ranka, Jinendra, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-Envelope Phase Control of Femtosecond ModeLocked Lasers and Direct Optical Frequency Synthesis," Science 288, 635–639 (2000).

59. S. Okubo, K. Gunji, A. Onae, M. Schramm, K. Nakamura, F. L. Hong, T. Hattori, K. Hosaka, and H. Inaba, "All-optically stabilized frequency comb," Appl. Phys. Express 8, 122701 (2015).

60. Y. Nakajima, H. Inaba, K. Hosaka, K. Minoshima, A. Onae, M. Yasuda, T. Kohno, S. Kawato, T. Kobayashi, T. Katsuyama, and F.-L. Hong, "A multibranch, fiber-based frequency comb with millihertz-level relative linewidths using an intra-cavity electro-optic modulator," Opt. Express 18, 1667–1676 (2010).

61. D. Akamatsu, M. Yasuda, T. Kohno, A. Onae, and F.-L. Hong, "A compact light source at 461 nm using a periodically poled LiNbO3 waveguide for strontium magneto-optical trapping.," Opt. Express 19, 2046–2051 (2011).

62. J. H. Shirley, "Modulation transfer processes in optical heterodyne saturation spectroscopy," Opt. Lett. 7, 537–539 (1982).

63. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser Phase and Frequency Stabilization Using an Optical Resonator," Appl. Phys. B 31, 97–105 (1983).

64. H. Inaba, K. Hosaka, M. Yasuda, Y. Nakajima, K. Iwakuni, D. Akamatsu, S. Okubo, T. Kohno, A. Onae, and F.-L. Hong, "Spectroscopy of 171Yb in an optical lattice based on laser linewidth transfer using a narrow linewidth frequency comb," Opt. Express 21, 7891–7896 (2013).

65. L.-S. Ma, P. Jungner, J. Ye, and J. L. Hall, "Delivering the same optical frequency at two places: accurate cancellation of phase noise introduced by an optical fiber or other time-varying path," Opt. Lett. 19, 1777–1779 (1994).

66. M. Takamoto, T. Takano, and H. Katori, "Frequency comparison of optical lattice clocks beyond the Dick limit," Nat. Photonics 5, 288–292 (2011).

67. T. Kobayashi, D. Akamatsu, K. Hosaka, and M. Yasuda, "A relocking scheme for optical phase locking using a digital circuit with an electrical delay line," Rev. Sci. Instrum. 90, 103002 (2019).

68. C. J. Foot, Atomic Physics (2005).

69. H. Katori, T. Ido, Y. Isoya, and M. Kuwata-gonokami, "Magneto-Optical Trapping and Cooling of Strontium Atoms down to the Photon Recoil Temperature," Phys. Rev. Lett. 82, 1116–1119 (1999).

70. M. M. Boyd, "High Precision Spectroscopy of Strontium in an Optical Lattice: Towards a New Standard for Frequency and Time," PhD thesis (2007).

71. T. Mukaiyama, H. Katori, T. Ido, Y. Li, and M. Kuwata-Gonokami, "RecoilLimited Laser Cooling of 87Sr Atoms near the Fermi Temperature," Phys. Rev. Lett. 90, 113002 (2003).

72. S. Friebel, C. D’Andrea, J. Walz, M. Weitz, and T. W. Hänsch, "CO2-laser optical lattice with cold rubidium atoms," Phys. Rev. A 57, R20–R23 (1998).

73. P. Lemonde and P. Wolf, "Optical lattice clock with atoms confined in a shallow trap," Phys. Rev. A 72, 033409 (2005).

74. R. H. Dicke, "The Effect of Collisions upon the Doppler Width of Spectral Lines," Phys. Rev. 89, 472–473 (1953).

75. M. Takamoto, F. L. Hong, R. Higashi, Y. Fujii, M. Imae, and H. Katori, "Improved frequency measurement of a one-dimensional optical lattice clock with a spin-polarized fermionic 87Sr isotope," J. Phys. Soc. Japan 75, 104302 (2006).

76. 大久保拓哉, "イッテルビウム・ストロンチウム光格子時計の時計遷移周波数比 測定," PhD thesis (2016).

77. S. Blatt, J. W. Thomsen, G. K. Campbell, A. D. Ludlow, M. D. Swallows, M. J. Martin, M. M. Boyd, and J. Ye, "Rabi spectroscopy and excitation inhomogeneity in a one-dimensional optical lattice clock," Phys. Rev. A 80, 052703 (2009).

78. Y. Hisai, D. Akamatsu, T. Kobayashi, K. Hosaka, H. Inaba, F.-L. Hong, and M. Yasuda, "Improved frequency ratio measurement with 87Sr and 171Yb optical lattice clocks at NMIJ," Metrologia 58, 015008 (2021).

79. I. Ushijima, M. Takamoto, and H. Katori, "Operational Magic Intensity for Sr Optical Lattice Clocks," Phys. Rev. Lett. 121, 263202 (2018).

80. S. G. Porsev and A. Derevianko, "Multipolar theory of blackbody radiation shift of atomic energy levels and its implications for optical lattice clocks," Phys. Rev. A 74, 020502 (2006).

81. M. S. Safronova, D. Jiang, B. Arora, C. W. Clark, M. G. Kozlov, U. I. Safronova, and W. R. Johnson, "Blackbody Radiation Shifts and Theoretical Contributions to Atomic Clock Research," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 94–105 (2010).

82. T. Middelmann, S. Falke, C. Lisdat, and U. Sterr, "High accuracy correction of blackbody radiation shift in an optical lattice clock," Phys. Rev. Lett. 109, 263004 (2012).

83. Joint Committee For Guides In Metrology, Evaluation of Measurement Data — Guide to the Expression of Uncertainty in Measurement (2008).

84. G. K. Campbell, M. M. Boyd, J. W. Thomsen, M. J. Martin, S. Blatt, M. D. Swallows, T. L. Nicholson, T. Fortier, C. W. Oates, S. A. Diddams, N. D. Lemke, P. Naidon, P. Julienne, J. Ye, and A. D. Ludlow, "Probing interactions between ultracold fermions," 324, 360–363 (2009).

85. M. J. Martin, "Quantum Metrology and Many-Body Physics : Pushing the Frontier of the Optical Lattice Clock," PhD thesis (2013).

86. M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. Blatt, T. Zanon-willette, S. M. Foreman, and J. Ye, "Nuclear spin effects in optical lattice clocks," Phys. Rev. A 76, 022510 (2007).

87. J. Lodewyck, M. Zawada, L. Lorini, M. Gurov, and P. Lemonde, "Observation and cancellation of a perturbing dc Stark shift in strontium optical lattice clocks," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 411–415 (2012).

88. W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, "Quantum projection noise: Population fluctuations in two-level systems," Phys. Rev. A 47, 3554–3570 (1993).

89. G. Santarelli, C. Audoin, A. Makdissi, P. Laurent, G. John Dick, and A. Clairon, "Frequency stability degradation of an oscillator slaved to a periodically interrogated atomic resonator," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 887–894 (1998).

90. A. Al-Masoudi, S. Dörscher, S. Häfner, U. Sterr, and C. Lisdat, "Noise and instability of an optical lattice clock," Phys. Rev. A 92, 063814 (2015).

91. C. Grebing, A. Al-Masoudi, S. Dörscher, S. Häfner, V. Gerginov, S. Weyers, B. Lipphardt, F. Riehle, U. Sterr, and C. Lisdat, "Realization of a timescale with an accurate optical lattice clock," Optica 3, 563–569 (2016).

92. M. Takamoto, I. Ushijima, M. Das, N. Nemitz, T. Ohkubo, K. Yamanaka, N. Ohmae, T. Takano, T. Akatsuka, A. Yamaguchi, and H. Katori, "Frequency ratios of Sr, Yb, and Hg based optical lattice clocks and their applications," Comptes Rendus Phys. 16, 489–498 (2015).

93. N. Nemitz, T. Ohkubo, M. Takamoto, I. Ushijima, M. Das, N. Ohmae, and H. Katori, "Frequency ratio of Yb and Sr clocks with 5 × 10-17 uncertainty at 150 seconds averaging time," Nat. Photonics 10, 258–261 (2016).

94. J. Grotti, S. Koller, S. Vogt, S. Häfner, U. Sterr, C. Lisdat, H. Denker, C. Voigt, L. Timmen, A. Rolland, F. N. Baynes, H. S. Margolis, M. Zampaolo, P. Thoumany, M. Pizzocaro, B. Rauf, F. Bregolin, A. Tampellini, P. Barbieri, M. Zucco, G. A. Costanzo, C. Clivati, F. Levi, and D. Calonico, "Geodesy and metrology with a transportable optical clock," Nat. Phys. 14, 437–441 (2018).

95. M. Fujieda, S. H. Yang, T. Gotoh, S. W. Hwang, H. Hachisu, H. Kim, Y. K. Lee, R. Tabuchi, T. Ido, W. K. Lee, M. S. Heo, C. Y. Park, D. H. Yu, and G. Petit, "Advanced Satellite-Based Frequency Transfer at the 10-16 Level," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 65, 973–978 (2018).

96. M. Pizzocaro, M. Sekido, K. Takefuji, H. Ujihara, H. Hachisu, N. Nemitz, M. Tsutsumi, T. Kondo, E. Kawai, R. Ichikawa, K. Namba, Y. Okamoto, R. Takahashi, J. Komuro, C. Clivati, F. Bregolin, P. Barbieri, A. Mura, E. Cantoni, G. Cerretto, F. Levi, G. Maccaferri, M. Roma, C. Bortolotti, M. Negusini, R. Ricci, G. Zacchiroli, J. Roda, J. Leute, G. Petit, F. Perini, D. Calonico, and T. Ido, "Intercontinental comparison of optical atomic clocks through very long baseline interferometry," Nat. Phys. 17, 223–227 (2020).

97. D. Akamatsu, T. Kobayashi, Y. Hisai, T. Tanabe, K. Hosaka, M. Yasuda, and F.- L. Hong, "Dual-mode operation of an optical lattice clock using strontium and ytterbium atoms," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 65, 1069– 1075 (2018).

98. R. Le Targat, X. Baillard, M. Fouché, A. Brusch, O. Tcherbakoff, G. D. Rovera, and P. Lemonde, "Accurate optical lattice clock with 87Sr atoms," Phys. Rev. Lett. 97, 130801 (2006).

99. A. D. Ludlow, M. M. Boyd, T. Zelevinsky, S. M. Foreman, S. Blatt, M. Notcutt, T. Ido, and J. Ye, "Systematic study of the 87Sr clock transition in an optical lattice," Phys. Rev. Lett. 96, 033003 (2006).

100. M. M. Boyd, A. D. Ludlow, S. Blatt, S. M. Foreman, T. Ido, T. Zelevinsky, and J. Ye, "87Sr Lattice Clock with Inaccuracy below 10-15," Phys. Rev. Lett. 98, 083002 (2007).

101. X. Baillard, M. Fouché, R. Le Targat, P. G. Westergaard, A. Lecallier, F. Chapelet, M. Abgrall, G. D. Rovera, P. Laurent, P. Rosenbusch, S. Bize, G. Santarelli, A. Clairon, P. Lemonde, G. Grosche, B. Lipphardt, and H. Schnatz, "An optical lattice clock with spin-polarized 87Sr atoms," Eur. Phys. J. D 48, 11– 17 (2008).

102. G. K. Campbell, A. D. Ludlow, S. Blatt, J. W. Thomsen, M. J. Martin, M. H. G. De Miranda, T. Zelevinsky, M. M. Boyd, J. Ye, S. A. Diddams, T. P. Heavner, T. E. Parker, and S. R. Jefferts, "The absolute frequency of the 87Sr optical clock transition," Metrologia 45, 539–548 (2008).

103. F. L. Hong, M. Musha, M. Takamoto, H. Inaba, S. Yanagimachi, A. Takamizawa, K. Watabe, T. Ikegami, M. Imae, Y. Fujii, M. Amemiya, K. Nakagawa, K. Ueda, and H. Katori, "Measuring the frequency of a Sr optical lattice clock using a 120 km coherent optical transfer," Opt. Lett. 34, 692–694 (2009).

104. S. Falke, H. Schnatz, J. S. R. V. Winfred, T. Middelmann, and S. Vogt, "The 87Sr optical frequency standard at PTB," Metrologia 48, 399–407 (2011).

105. K. Matsubara, H. Hachisu, Y. Li, S. Nagano, C. Locke, A. Nogami, M. Kajita, K. Hayasaka, T. Ido, and M. Hosokawa, "Direct comparison of a Ca+ single-ion clock against a Sr lattice clock to verify the absolute frequency measurement," Opt. Express 20, 22034–22041 (2012).

106. R. Le Targat, L. Lorini, Y. Le Coq, M. Zawada, J. Guéna, M. Abgrall, M. Gurov, P. Rosenbusch, D. G. Rovera, B. Nagórny, R. Gartman, P. G. Westergaard, M. E. Tobar, M. Lours, G. Santarelli, A. Clairon, S. Bize, P. Laurent, P. Lemonde, and J. Lodewyck, "Experimental realization of an optical second with strontium lattice clocks," Nat. Commun. 4, 2109 (2013).

107. S. Falke, N. Lemke, C. Grebing, B. Lipphardt, S. Weyers, V. Gerginov, N. Huntemann, C. Hagemann, A. Al-Masoudi, S. Häfner, S. Vogt, U. Sterr, and C. Lisdat, "A strontium lattice clock with 3 × 10-17 inaccuracy and its frequency," New J. Phys. 16, 073023 (2014).

108. Y. G. Lin, Q. Wang, Y. Li, F. Meng, B. K. Lin, E. J. Zang, Z. Sun, F. Fang, T. C. Li, and Z. J. Fang, "First Evaluation and Frequency Measurement of the Strontium Optical Lattice Clock at NIM," Chinese Phys. Lett. 32, 090601 (2015).

109. H. Hachisu and T. Ido, "Intermittent optical frequency measurements to reduce the dead time uncertainty of frequency link," Jpn. J. Appl. Phys. 54, 112401 (2015).

110. T. Tanabe, D. Akamatsu, T. Kobayashi, A. Takamizawa, S. Yanagimachi, T. Ikegami, T. Suzuyama, H. Inaba, S. Okubo, M. Yasuda, F. L. Hong, A. Onae, and K. Hosaka, "Improved Frequency Measurement of the 1S0- 3P0 Clock Transition in 87Sr Using a Cs Fountain Clock as a Transfer Oscillator," J. Phys. Soc. Japan 84, 115002 (2015).

111. J. Lodewyck, S. Bilicki, E. Bookjans, J.-L. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guéna, M. Abgrall, P. Rosenbusch, and S. Bize, "Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock," Metrologia 53, 1123–1130 (2016).

112. H. Hachisu, G. Petit, and T. Ido, "Absolute frequency measurement with uncertainty below 1 × 10-15 using International Atomic Time," Appl. Phys. B 123, 34 (2017).

113. H. Hachisu, G. Petit, F. Nakagawa, Y. Hanado, and T. Ido, "SI-traceable measurement of an optical frequency at the low 10-16 level without a local primary standard," Opt. Express 25, 8511–8523 (2017).

114. R. Schwarz, S. Dörscher, A. Al-Masoudi, E. Benkler, T. Legero, U. Sterr, S. Weyers, J. Rahm, B. Lipphardt, and C. Lisdat, "Long term measurement of the 87Sr clock frequency at the limit of primary Cs clocks," Phys. Rev. Res. 2, 033242 (2020).

115. R. Hobson, W. Bowden, A. Vianello, A. Silva, C. Baynham, H. S. Margolis, P. E. G. Baird, P. Gill, and I. R. Hill, "A strontium optical lattice clock with 1 × 10-17 uncertainty and measurement of its absolute frequency," Metrologia 57, 065026 (2020).

116. K. R. Parameswaran, J. R. Kurz, R. V. Roussev, and M. M. Fejer, "Observation of 99% pump depletion in single-pass second-harmonic generation in a periodically poled lithium niobate waveguide," Opt. Lett. 27, 43–45 (2002).