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88Sr+ optical clock with 7.9×10−19 systematic uncertainty and measurement of its absolute frequency with 9.8×10−17 uncertainty

T. Lindvall1,*, T. Fordell1, K.J. Hanhijärvi1, M. Doležal2, J. Rahm3, S. Weyers3, and A.E. Wallin1

  • *Contact author: thomas.lindvall@vtt.fi
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Phys. Rev. Applied 24, 044082 – Published 27 October, 2025

DOI: https://doi.org/10.1103/czlf-bfvp

Abstract

We report on a 88Sr+ single-ion optical clock with an estimated fractional systematic uncertainty of 7.9×10−19. The low uncertainty is enabled by small rf losses, a thorough evaluation of the blackbody-radiation temperature, and our recent measurement of the differential polarizability. A detailed uncertainty evaluation is presented. We also report on two absolute frequency measurements: one against a remote cesium fountain clock, and one against International Atomic Time (TAI). The former lasted 12 d and resulted in a frequency value of 444 779 044 095 485.49(15) Hz. The latter spanned 10 months with monthly optical-clock uptimes between 68% and 99%, and yielded a frequency value of 444 779 044 095 485.373(44) Hz. With a fractional uncertainty of 9.8×10−17, it is, to our knowledge, the most accurate optical frequency measurement reported to date. Both frequency values are in agreement with other recent measurements, providing further evidence that the 2021 CIPM recommended frequency value is too high by 1.6 times its uncertainty.

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References (119)

  1. A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, Optical atomic clocks, Rev. Mod. Phys. 87, 637 (2015).
  2. 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, 27Al+ quantum-logic clock with a systematic uncertainty below 10−18, Phys. Rev. Lett. 123, 033201 (2019).
  3. A. Aeppli, K. Kim, W. Warfield, M. S. Safronova, and J. Ye, Clock with 8×10−19 systematic uncertainty, Phys. Rev. Lett. 133, 023401 (2024).
  4. M. C. Marshall, D. A. R. Castillo, W. J. Arthur-Dworschack, A. Aeppli, K. Kim, D. Lee, W. Warfield, J. Hinrichs, N. V. Nardelli, T. M. Fortier, J. Ye, D. R. Leibrandt, and D. B. Hume, High-stability single-ion clock with 5.5×10−19 systematic uncertainty, Phys. Rev. Lett. 135, 033201 (2025).
  5. B. Zhang, Z. Ma, Y. Huang, H. Han, R. Hu, Y. Wang, H. Zhang, L. Tang, T. Shi, H. Guan, and K. Gao, A liquid-nitrogen-cooled Ca+ ion optical clock with a systematic uncertainty of 4.6×10−19, arXiv:2506.17423.
  6. P. Delva, J. Lodewyck, S. Bilicki, E. Bookjans, G. Vallet, R. Le Targat, P.-E. Pottie, C. Guerlin, F. Meynadier, C. Le Poncin-Lafitte, et al., Test of special relativity using a fiber network of optical clocks, Phys. Rev. Lett. 118, 221102 (2017).
  7. 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 (2019).
  8. R. Lange, N. Huntemann, J. M. Rahm, C. Sanner, H. Shao, B. Lipphardt, C. Tamm, S. Weyers, and E. Peik, Improved limits for violations of local position invariance from atomic clock comparisons, Phys. Rev. Lett. 126, 011102 (2021).
  9. N. Sherrill, A. O. Parsons, C. F. A. Baynham, W. Bowden, E. A. Curtis, R. Hendricks, I. R. Hill, R. Hobson, H. S. Margolis, B. I. Robertson, M. Schioppo, K. Szymaniec, A. Tofful, J. Tunesi, R. M. Godun, and X. Calmet, Analysis of atomic-clock data to constrain variations of fundamental constants, New J. Phys. 25, 093012 (2023).
  10. B. M. Roberts, P. Delva, A. Al-Masoudi, A. Amy-Klein, C. Bærentsen, C. F. A. Baynham, E. Benkler, S. Bilicki, S. Bize, W. Bowden, et al., Search for transient variations of the fine structure constant and dark matter using fiber-linked optical atomic clocks, New J. Phys. 22, 093010 (2020).
  11. C. J. Kennedy, E. Oelker, J. M. Robinson, T. Bothwell, D. Kedar, W. R. Milner, G. E. Marti, A. Derevianko, and J. Ye, Precision metrology meets cosmology: Improved constraints on ultralight dark matter from atom-cavity frequency comparisons, Phys. Rev. Lett. 125, 201302 (2020).
  12. K. Beloy, M. I. Bodine, T. Bothwell, S. M. Brewer, S. L. Bromley, J.-S. Chen, J.-D. Deschênes, S. A. Diddams, R. J. Fasano, T. M. Fortier, et al. BACON Collaboration, Frequency ratio measurements at 18-digit accuracy using an optical clock network, Nature 591, 564 (2021).
  13. T. Kobayashi, A. Takamizawa, D. Akamatsu, A. Kawasaki, A. Nishiyama, K. Hosaka, Y. Hisai, M. Wada, H. Inaba, T. Tanabe, and M. Yasuda, Search for ultralight dark matter from long-term frequency comparisons of optical and microwave atomic clocks, Phys. Rev. Lett. 129, 241301 (2022).
  14. M. Filzinger, S. Dörscher, R. Lange, J. Klose, M. Steinel, E. Benkler, E. Peik, C. Lisdat, and N. Huntemann, Improved limits on the coupling of ultralight bosonic dark matter to photons from optical atomic clock comparisons, Phys. Rev. Lett. 130, 253001 (2023).
  15. C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, Frequency comparison of two high-accuracy Al+ optical clocks, Phys. Rev. Lett. 104, 070802 (2010).
  16. J. Grotti, S. Koller, S. Vogt, S. Häfner, U. Sterr, C. Lisdat, H. Denker, C. Voigt, L. Timmen, A. Rolland, et al., Geodesy and metrology with a transportable optical clock, Nat. Phys. 14, 437 (2018).
  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 (2020).
  18. J. Grotti, I. Nosske, S. B. Koller, S. Herbers, H. Denker, L. Timmen, G. Vishnyakova, G. Grosche, T. Waterholter, A. Kuhl, et al., Long-distance chronometric leveling with a portable optical clock, Phys. Rev. Appl. 21, L061001 (2024).
  19. N. Dimarcq, M. Gertsvolf, G. Mileti, S. Bize, C. W. Oates, E. Peik, D. Calonico, T. Ido, P. Tavella, F. Meynadier, et al., Roadmap towards the redefinition of the second, Metrologia 61, 012001 (2024).
  20. A. Tofful, C. F. A. Baynham, E. A. Curtis, A. O. Parsons, B. I. Robertson, M. Schioppo, J. Tunesi, H. S. Margolis, R. J. Hendricks, J. Whale, R. C. Thompson, and R. M. Godun, 171Yb+ optical clock with 2.2×10−18 systematic uncertainty and absolute frequency measurements, Metrologia 61, 045001 (2024).
  21. H. Hausser, J. Keller, T. Nordmann, N. Bhatt, J. Kiethe, H. Liu, I. Richter, M. von Boehn, J. Rahm, S. Weyers, E. Benkler, B. Lipphardt, S. Dörscher, K. Stahl, J. Klose, C. Lisdat, M. Filzinger, N. Huntemann, E. Peik, and T. Mehlstäubler, 115In+–172Yb+ Coulomb crystal clock with 2.5×10−18 systematic uncertainty, Phys. Rev. Lett. 134, 023201 (2025).
  22. 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 (2018).
  23. 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).
  24. X. Lu, F. Guo, Y. Liu, J. Cao, J. Li, J. Xia, Q. Xu, B. Lu, Y. Wang, and H. Chang, NTSC SrII optical lattice clock with uncertainty of 2×10−18, Metrologia 62, 035007 (2025).
  25. P. Dubé, A. A. Madej, J. E. Bernard, L. Marmet, J.-S. Boulanger, and S. Cundy, Electric quadrupole shift cancellation in single-ion optical frequency standards, Phys. Rev. Lett. 95, 033001 (2005).
  26. T. Lindvall, K. J. Hanhijärvi, T. Fordell, and A. E. Wallin, High-accuracy determination of Paul-trap stability parameters for electric-quadrupole-shift prediction, J. Appl. Phys. 132, 124401 (2022).
  27. P. Dubé, A. A. Madej, M. Tibbo, and J. E. Bernard, in 2014 European Frequency and Time Forum (EFTF) (IEEE, Piscataway, NJ, 2014), p. 443.
  28. H. C. J. Gan, G. Maslennikov, K.-W. Tseng, T. R. Tan, R. Kaewuam, K. J. Arnold, D. Matsukevich, and M. D. Barrett, Oscillating-magnetic-field effects in high-precision metrology, Phys. Rev. A 98, 032514 (2018).
  29. T. Lindvall, K. J. Hanhijärvi, T. Fordell, and A. E. Wallin, Measurement of the differential static scalar polarizability of the 88Sr+ clock transition, Phys. Rev. Lett. 135, 043402 (2025).
  30. P. Dubé, K. Kato, J. Bernard, and B. Jian, in 2021 Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS) (IEEE, Piscataway, NJ, 2021).
  31. A. Spampinato, J. Stacey, S. Mulholland, B. I. Robertson, H. A. Klein, G. Huang, G. P. Barwood, and P. Gill, An ion trap design for a space-deployable strontium-ion optical clock, Proc. R. Soc. A 480, 20230593 (2024).
  32. D. Fairbank, D. Lee, M. Notcutt, and J. Davila-Rodriguez, in IFCS-EFTF 2025 (2025).
  33. M. Steinel, H. Shao, M. Filzinger, B. Lipphardt, M. Brinkmann, A. Didier, T. E. Mehlstäubler, T. Lindvall, E. Peik, and N. Huntemann, Evaluation of a 88Sr+ optical clock with a direct measurement of the blackbody radiation shift and determination of the clock frequency, Phys. Rev. Lett. 131, 083002 (2023).
  34. N. Akerman and R. Ozeri, Operating a multi-ion clock with dynamical decoupling, Phys. Rev. Lett. 134, 013201 (2025).
  35. W. Loh, D. Reens, D. Kharas, A. Sumant, C. Belanger, R. T. Maxson, A. Medeiros, W. Setzer, D. Gray, K. DeBry, et al., Optical atomic clock interrogation using an integrated spiral cavity laser, Nat. Photonics 19, 277 (2025).
  36. B. Jian, J. Bernard, M. Gertsvolf, and P. Dubé, Improved absolute frequency measurement of the strontium ion clock using a GPS link to the SI second, Metrologia 60, 015007 (2023).
  37. G. P. Barwood, G. Huang, S. A. King, H. A. Klein, and P. Gill, Frequency noise processes in a strontium ion optical clock, J. Phys. B: At. Mol. Opt. Phys. 48, 035401 (2015).
  38. M. Zeng, Z. Ma, R. Hu, B. Zhang, Y. Hao, H. Zhang, Y. Huang, H. Guan, and K. Gao, A combined magnetic field stabilization system for improving the stability of 40Ca+ optical clock, Chinese Phys. B 32, 110704 (2023).
  39. 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 (2018).
  40. G. Petit, A. Kanj, S. Loyer, J. Delporte, F. Mercier, and F. Perosanz, 1×10−16 frequency transfer by GPS PPP with integer ambiguity resolution, Metrologia 52, 301 (2015).
  41. W. F. McGrew, X. Zhang, H. Leopardi, R. J. Fasano, D. Nicolodi, K. Beloy, J. Yao, J. A. Sherman, S. A. Schäffer, J. Savory, R. C. Brown, S. Römisch, C. W. Oates, T. E. Parker, T. M. Fortier, and A. D. Ludlow, Towards the optical second: Verifying optical clocks at the SI limit, Optica 6, 448 (2019).
  42. 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).
  43. N. Nemitz, T. Gotoh, F. Nakagawa, H. Ito, Y. Hanado, T. Ido, and H. Hachisu, Absolute frequency of 87Sr at 1.8×10−16 uncertainty by reference to remote primary frequency standards, Metrologia 58, 025006 (2021).
  44. T. Kobayashi, A. Nishiyama, K. Hosaka, D. Akamatsu, A. Kawasaki, M. Wada, H. Inaba, T. Tanabe, and M. Yasuda, Improved absolute frequency measurement of 171Yb at NMIJ with uncertainty below 2×10−16, Metrologia 62, 025006 (2025).
  45. C. Marceau, S. Beattie, K. Kato, B. Jian, M. Gertsvolf, and P. Dubé, Absolute frequency measurement of a 88Sr+ clock by direct comparison to a primary frequency standard, Metrologia 62, 045001 (2025).
  46. M. Brownnutt, V. Letchumanan, G. Wilpers, R. C. Thompson, P. Gill, and A. G. Sinclair, Controlled photoionization loading of 88Sr+ for precision ion-trap experiments, Appl. Phys. B 87, 411 (2007).
  47. T. Fordell and T. Lindvall, Broadband lasers for photo-ionization and repumping of trapped ions, J. Opt. Soc. Am. B 36, 415 (2019).
  48. S.-U. Haq, S. Mahmood, N. Amin, Y. Jamil, R. Ali, and M. A. Baig, Measurements of photoionization cross sections from the 5s5p1P1 and 5s6s1S0 excited states of strontium, J. Phys. B: At. Mol. Opt. Phys. 39, 1587 (2006).
  49. A. D. Shiner, A. A. Madej, P. Dubé, and J. E. Bernard, Absolute optical frequency measurement of saturated absorption lines in Rb near 422 nm, Appl. Phys. B 89, 595 (2007).
  50. T. Lindvall, T. Fordell, I. Tittonen, and M. Merimaa, Unpolarized, incoherent repumping light for prevention of dark states in a trapped and laser-cooled single ion, Phys. Rev. A 87, 013439 (2013).
  51. T. Fordell, T. Lindvall, P. Dubé, A. A. Madej, A. E. Wallin, and M. Merimaa, Broadband, unpolarized repumping and clearout light sources for Sr+ single-ion clocks, Opt. Lett. 40, 1822 (2015).
  52. T. Lindvall, M. Merimaa, I. Tittonen, and A. A. Madej, Dark-state suppression and optimization of laser cooling and fluorescence in a trapped alkaline-earth-metal single ion, Phys. Rev. A 86, 033403 (2012).
  53. S. Häfner, S. Falke, C. Grebing, S. Vogt, T. Legero, M. Merimaa, C. Lisdat, and U. Sterr, 8×10−17 fractional laser frequency instability with a long room-temperature cavity, Opt. Lett. 40, 2112 (2015).
  54. Martin Steinel (private communication).
  55. T. Lindvall, A. E. Wallin, K. J. Hanhijärvi, and T. Fordell, Noise-induced servo errors in optical clocks utilizing Rabi interrogation, Metrologia 60, 045008 (2023).
  56. S. Bourdeauducq, R. Jördens, P. Zotov, J. Britton, D. Slichter, D. Leibrandt, D. Allcock, A. Hankin, F. Kermarrec, Y. Sionneau, R. Srinivas, T. R. Tan, and J. Bohnet, ARTIQ 1.0, 2016, https://doi.org/10.5281/zenodo.51303.
  57. H. Wu, M. Mills, E. West, M. C. Heaven, and E. R. Hudson, Increase of the barium ion-trap lifetime via photodissociation, Phys. Rev. A 104, 063103 (2021).
  58. P. Dubé, A. A. Madej, A. Shiner, and B. Jian, 88Sr+ single-ion optical clock with a stability approaching the quantum projection noise limit, Phys. Rev. A 92, 042119 (2015).
  59. P. Dubé, A. A. Madej, Z. Zhou, and J. E. Bernard, Evaluation of systematic shifts of the 88Sr+ single-ion optical frequency standard at the 10−17 level, Phys. Rev. A 87, 023806 (2013).
  60. D. J. Berkeland, J. D. Miller, J. C. Bergquist, W. M. Itano, and D. J. Wineland, Minimization of ion micromotion in a Paul trap, J. Appl. Phys. 83, 5025 (1998).
  61. J. Keller, H. L. Partner, T. Burgermeister, and T. E. Mehlstäubler, Precise determination of micromotion for trapped-ion optical clocks, J. Appl. Phys. 118, 104501 (2015).
  62. P. Dubé, A. A. Madej, M. Tibbo, and J. E. Bernard, High-accuracy measurement of the differential scalar polarizability of a 88Sr+ clock using the time-dilation effect, Phys. Rev. Lett. 112, 173002 (2014).
  63. P. Barakhshan, A. Marrs, A. Bhosale, B. Arora, R. Eigenmann, and M. S. Safronova, Portal for High-Precision Atomic Data and Computation (version 2.0). University of Delaware, Newark, Delaware. https://www.udel.edu/atom (February 2022).
  64. M. Brownnutt, M. Kumph, P. Rabl, and R. Blatt, Ion-trap measurements of electric-field noise near surfaces, Rev. Mod. Phys. 87, 1419 (2015).
  65. M. Doležal, P. Balling, P. B. R. Nisbet-Jones, S. A. King, J. M. Jones, H. A. Klein, P. Gill, T. Lindvall, A. E. Wallin, M. Merimaa, C. Tamm, C. Sanner, N. Huntemann, N. Scharnhorst, I. D. Leroux, P. O. Schmidt, T. Burgermeister, T. E. Mehlstäubler, and E. Peik, Analysis of thermal radiation in ion traps for optical frequency standards, Metrologia 52, 842 (2015).
  66. M. Abdel-Hafiz, P. Ablewski, A. Al-Masoudi, H. Álvarez Martínez, P. Balling, G. Barwood, E. Benkler, M. Bober, M. Borkowski, W. Bowden, et al., Guidelines for developing optical clocks with 10−18 fractional frequency uncertainty, edited by T. Lindvall, arXiv:1906.11495.
  67. P. B. R. Nisbet-Jones, S. A. King, J. M. Jones, R. M. Godun, C. F. A. Baynham, K. Bongs, M. Doležal, P. Balling, and P. Gill, A single-ion trap with minimized ion–environment interactions, Appl. Phys. B 122, 57 (2016).
  68. T. Nordmann, A. Didier, M. Doležal, P. Balling, T. Burgermeister, and T. E. Mehlstäubler, Sub-kelvin temperature management in ion traps for optical clocks, Rev. Sci. Instrum. 91, 111301 (2020).
  69. P. Ablewski, M. Bober, and M. Zawada, Emissivities of vacuum compatible materials: Towards minimising blackbody radiation shift uncertainty in optical atomic clocks at room temperatures, Metrologia 57, 035004 (2020).
  70. C. Gaiser, B. Fellmuth, R. M. Gavioso, M. Kalemci, V. Kytin, T. Nakano, A. Pokhodun, P. M. C. Rourke, R. Rusby, F. Sparasci, P. P. M. Steur, W. L. Tew, R. Underwood, R. White, I. Yang, and J. Zhang, 2022 update for the differences between thermodynamic temperature and ITS-90 below 335 K, J. Phys. Chem. Ref. Data 51, 043105 (2022).
  71. J. E. Sansonetti, Wavelengths, transition probabilities, and energy levels for the spectra of strontium ions (Sr II through Sr XXXVIII), J. Phys. Chem. Ref. Data 41, 013102 (2012).
  72. J. W. Farley and W. H. Wing, Accurate calculation of dynamic Stark shifts and depopulation rates of Rydberg energy levels induced by blackbody radiation. Hydrogen, helium, and alkali-metal atoms, Phys. Rev. A 23, 2397 (1981).
  73. 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).
  74. B. Arora, D. K. Nandy, and B. K. Sahoo, Multipolar blackbody radiation shifts for single-ion clocks, Phys. Rev. A 85, 012506 (2012).
  75. U. I. Safronova and M. S. Safronova, Excitation energies, E1, M1, and E2 transition rates, and lifetimes in Ca+, Sr+, Cd+, Ba+, and Hg+, Can. J. Phys. 89, 465 (2011).
  76. Z.-M. Tang, Y.-F. Wei, B. K. Sahoo, C.-B. Li, Y. Yang, Y. Zou, and X.-R. Huang, Blackbody-radiation Zeeman shifts in optical clocks: The role of fine-structure intramanifold resonances, Phys. Rev. A 110, 043108 (2024).
  77. K. J. Arnold, R. Kaewuam, S. R. Chanu, T. R. Tan, Z. Zhang, and M. D. Barrett, Precision measurements of the 138Ba+6s2S1/2–5d2D5/2 clock transition, Phys. Rev. Lett. 124, 193001 (2020).
  78. E. A. Curtis, A. Tofful, A. O. Parsons, B. I. Robertson, and R. M. Godun, 171Yb+ ion optical clock at NPL: Advances in automation and assessment of the trap-induced ac Zeeman shift in an endcap trap geometry, J. Phys. Conf. Ser. 2889, 012044 (2024).
  79. M. Ivory, C. D. Nordquist, K. Young, C. W. Hogle, S. M. Clark, and M. C. Revelle, AC Zeeman effect in microfabricated surface traps, Rev. Sci. Instrum. 95, 093202 (2024).
  80. D. F. V. James, Quantum dynamics of cold trapped ions with application to quantum computation, Appl. Phys. B 66, 181 (1998).
  81. U. I. Safronova, M. S. Safronova, and W. R. Johnson, Forbidden M1 and E2 transitions in monovalent atoms and ions, Phys. Rev. A 95, 042507 (2017).
  82. V. I. Yudin, A. V. Taichenachev, O. N. Prudnikov, M. Y. Basalaev, V. G. Pal’chikov, M. von Boehn, T. E. Mehlstäubler, and S. N. Bagayev, Probe-field-ellipticity-induced shift in an atomic clock, Phys. Rev. Appl. 19, 014022 (2023).
  83. B. M. Roberts, C. J. Fairhall, and J. S. M. Ginges, Electric-dipole transition amplitudes for atoms and ions with one valence electron, Phys. Rev. A 107, 052812 (2023).
  84. R. Kersevan and M. Ady, in Proceedings of the 10th Int. Particle Accelerator Conf., IPAC2019, Australia (JACoW Publishing, Geneva, Switzerland, 2019).
  85. J.-P. Likforman, V. Tugayé, S. Guibal, and L. Guidoni, Precision measurement of the branching fractions of the 5p2P1/2 state in 88Sr+ with a single ion in a microfabricated surface trap, Phys. Rev. A 93, 052507 (2016).
  86. P. A. Barton, C. J. S. Donald, D. M. Lucas, D. A. Stevens, A. M. Steane, and D. N. Stacey, Measurement of the lifetime of the 3d2D5/2 state in 40Ca+, Phys. Rev. A 62, 032503 (2000).
  87. G. Pagano, P. W. Hess, H. B. Kaplan, W. L. Tan, P. Richerme, P. Becker, A. Kyprianidis, J. Zhang, E. Birckelbaw, M. R. Hernandez, Y. Wu, and C. Monroe, Cryogenic trapped-ion system for large scale quantum simulation, Quantum Sci. Technol. 4, 014004 (2019).
  88. A. M. Hankin, E. R. Clements, Y. Huang, S. M. Brewer, J.-S. Chen, C. W. Chou, D. B. Hume, and D. R. Leibrandt, Systematic uncertainty due to background-gas collisions in trapped-ion optical clocks, Phys. Rev. A 100, 033419 (2019).
  89. N. Lagakos, J. A. Bucaro, and J. Jarzynski, Temperature-induced optical phase shifts in fibers, Appl. Opt. 20, 2305 (1981).
  90. T. Lindvall, M. Pizzocaro, R. M. Godun, M. Abgrall, D. Akamatsu, A. Amy-Klein, E. Benkler, N. Bhatt, D. Calonico, E. Cantin, et al., Coordinated international comparisons between optical clocks connected via fiber and satellite links, Optica 12, 843 (2025).
  91. H. S. Margolis, R. M. Godun, N. Huntemann, R. Le Targat, M. Pizzocaro, M. Zawada, M. Abgrall, D. Akamatsu, H. Álvarez Martínez, A. Amy-Klein, et al., Robust optical clocks for international timescales (ROCIT), J. Phys. Conf. Ser. 2889, 012022 (2024).
  92. T. Lindvall and A. E. Wallin, Zenodo, http://doi.org/10.5281/zenodo.17070662, 2025.
  93. H. Denker, L. Timmen, C. Voigt, S. Weyers, E. Peik, H. S. Margolis, P. Delva, P. Wolf, and G. Petit, Geodetic methods to determine the relativistic redshift at the level of 10−18 in the context of international timescales: A review and practical results, J. Geod. 92, 487 (2018).
  94. 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 (2017).
  95. 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).
  96. Circular T is a monthly publication by the Bureau International des Poids et Mesures (BIPM), available at https://www.bipm.org/en/time-ftp/circular-t.
  97. S. T. Dawkins, J. J. McFerran, and A. N. Luiten, Considerations on the measurement of the stability of oscillators with frequency counters, IEEE Trans. Ultrason., Ferroelectr., Freq. Control 54, 918 (2007).
  98. Files reporting the fractional frequency of EAL per Circular T month. Also list uA, uB, and weights of all contributing PSFSs. Available at https://webtai.bipm.org/ftp/pub/tai/other-products/etoile/.
  99. G. Panfilo and T. E. Parker, A theoretical and experimental analysis of frequency transfer uncertainty, including frequency transfer into TAI, Metrologia 47, 552 (2010).
  100. M. G. Cox, C. Eiø, G. Mana, and F. Pennecchi, The generalized weighted mean of correlated quantities, Metrologia 43, S268 (2006).
  101. H. S. Margolis, G. Panfilo, G. Petit, C. Oates, T. Ido, and S. Bize, The CIPM list “Recommended values of standard frequencies”: 2021 update, Metrologia 61, 035005 (2024).
  102. 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 (2004).
  103. A. A. Madej, P. Dubé, Z. Zhou, J. E. Bernard, and M. Gertsvolf, 88Sr+ 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 (2012).
  104. G. P. Barwood, G. Huang, H. A. Klein, L. A. M. Johnson, S. A. King, H. S. Margolis, K. Szymaniec, and P. Gill, Agreement between two 88Sr+ optical clocks to 4 parts in 1017, Phys. Rev. A 89, 050501 (2014).
  105. P. Dubé, J. E. Bernard, and M. Gertsvolf, Absolute frequency measurement of the 88Sr+ clock transition using a GPS link to the SI second, Metrologia 54, 290 (2017).
  106. D. Jiang, B. Arora, M. S. Safronova, and C. W. Clark, Blackbody-radiation shift in a 88Sr+ ion optical frequency standard, J. Phys. B: At. Mol. Opt. Phys. 42, 154020 (2009).
  107. N. Nemitz, H. Hachisu, H. Ito, N. Ohtsubo, Y. Miyauchi, M. Morikawa, K. Matsubara, and T. Ido, Hydrogen maser flywheels for optical clocks, J. Phys. Conf. Ser. 2889, 012019 (2024).
  108. G. J. Dick, in Proceedings of the Nineteenth Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting (U.S. Naval Observatory, Washington D.C., Redondo Beach, CA, 1987), p. 133.
  109. O. Vestøl, J. Ågren, H. Steffen, H. Kierulf, and L. Tarasov, NKG2016LU: A new land uplift model for Fennoscandia and the Baltic region, J. Geod. 93, 1759 (2019).
  110. P. Häkli, K. Evers, L. Jivall, T. Nilsson, S. Himle, K. Kollo, I. Liepiņš, E. Paršeliūnas, O. Vestøl, and M. Lidberg, NKG2020 transformation: An updated transformation between dynamic and static reference frames in the Nordic and Baltic countries, J. Geod. Sci. 13, 20220155 (2023).
  111. I. Y. Blinov, A. I. Boiko, Y. S. Domnin, V. P. Kostromin, O. V. Kupalova, and D. S. Kupalov, Budget of uncertainties in the cesium frequency frame of fountain type, Meas. Tech. 60, 30 (2017).
  112. S. Beattie, B. Jian, J. Alcock, M. Gertsvolf, R. Hendricks, K. Szymaniec, and K. Gibble, First accuracy evaluation of the NRC-FCs2 primary frequency standard, Metrologia 57, 035010 (2020).
  113. J. Guéna, M. Abgrall, D. Rovera, P. Laurent, B. Chupin, M. Lours, G. Santarelli, P. Rosenbusch, M. Tobar, R. Li, K. Gibble, A. Clairon, and S. Bize, Progress in atomic fountains at LNE-SYRTE, IEEE Trans. Ultrason., Ferroelectr., Freq. Control 59, 391 (2012).
  114. J. Guéna, M. Abgrall, A. Clairon, and S. Bize, Contributing to TAI with a secondary representation of the SI second, Metrologia 51, 108 (2014).
  115. X.-L. Wang, J. Ruan, D.-D. Liu, Y. Guan, J.-R. Shi, F. Yang, Y. Bai, H. Zhang, S.-C. Fan, W.-J. Wu, S.-H. Zhao, and S.-G. Zhang, First evaluation of the primary frequency standard NTSC-CsF2, Metrologia 60, 065012 (2023).
  116. F. Levi, D. Calonico, C. E. Calosso, A. Godone, S. Micalizio, and G. A. Costanzo, Accuracy evaluation of ITCsF2: A nitrogen cooled caesium fountain, Metrologia 51, 270 (2014).
  117. F. Fang, M. Li, P. Lin, W. Chen, N. Liu, Y. Lin, P. Wang, K. Liu, R. Suo, and T. Li, NIM5 Cs fountain clock and its evaluation, Metrologia 52, 454 (2015).
  118. R. Hobson, W. Bowden, A. Vianello, A. Silva, C. F. A. 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).
  119. A. Jallageas, L. Devenoges, M. Petersen, J. Morel, L. G. Bernier, D. Schenker, P. Thomann, and T. Südmeyer, First uncertainty evaluation of the FoCS-2 primary frequency standard, Metrologia 55, 366 (2018).

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Phys. Rev. Applied 24, 044082– Published 27 October, 2025
  • Received 7 July 2025
  • Revised 27 August 2025
  • Accepted 5 September 2025
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