Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

High-stability optical clock based on a continuously ground-state cooled Al+ ion without compromising its accuracy

Fabian Dawel1,2, Lennart Pelzer1, Kai Dietze1,2, Johannes Kramer1,2, Marek Hild1, Steven A. King1,*, Nicolas C. H. Spethmann1, Joshua Klose1, Kilian Stahl1 et al.

Sören Dörscher1, Erik Benkler1, Christian Lisdat1, Sergey G. Porsev3, Marianna S. Safronova3,†, and Piet O. Schmidt1,2,‡

  • *Present address: Oxford Ionics, Oxford OX5 1GN, United Kingdom.
  • †Contact author: msafrono@udel.edu
  • ‡Contact author: Piet.Schmidt@quantummetrology.de

Phys. Rev. Research 8, 023327 – Published 23 June, 2026

DOI: https://doi.org/10.1103/48zr-2t1p

Abstract

Single-ion optical clocks have shown systematic frequency uncertainties below 10−18, but typically require more than one week of averaging to achieve a corresponding statistical uncertainty. This time can be reduced with longer probe times, but comes at the cost of a higher time-dilation shift due to motional heating of the ions in the trap. We show that sympathetic ground-state cooling using electromagnetically induced transparency of an Al+ clock ion via a cotrapped Ca+ ion during clock interrogation suppresses the heating of the ions. Al+ can be kept close to the motional ground state, independent from the chosen interrogation time, at a relative time-dilation shift of (−1.69±0.20)×10−18. The Ca+ cooling light introduces an additional light shift on the Al+ clock transition of (−9.3±1.1)×10−18. We project that the uncertainty of this light shift can be further reduced by nearly an order of magnitude. This sympathetic cooling enables seconds of interrogation time with 10−19 motional and cooling laser-induced uncertainties for Al+ and can be employed in other ion clocks as well.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (81)

  1. 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).
  2. A. Aeppli, K. Kim, W. Warfield, M. S. Safronova, and J. Ye, A clock with 8×10−19 systematic uncertainty, Phys. Rev. Lett. 133, 023401 (2024).
  3. 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).
  4. K. J. Arnold, S. Bustabad, Z. Qi, Q. Qichen, Z. Zhang, Z. Zhao, and M. D. Barrett, Validating a lutetium frequency reference, J. Phys.: Conf. Ser. 2889, 012040 (2024).
  5. 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 (London) 564, 87 (2018).
  6. 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 (London) 567, 204 (2019).
  7. 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. Photon. 14, 411 (2020).
  8. H. N. Hausser, J. Keller, T. Nordmann, N. M. Bhatt, J. Kiethe, H. Liu, I. M. 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. E. Mehlstäubler, In+115–Yb+172 Coulomb crystal clock with 2.5×10−18 systematic uncertainty, Phys. Rev. Lett. 134, 023201 (2025).
  9. A. Amy-Klein, E. Benkler, P. Blondé, K. Bongs, E. Cantin, C. Chardonnet, H. Denker, S. Dörscher, C.-H. Feng, J.-O. Gaudron, et al., International comparison of optical frequencies with transportable optical lattice clocks, arXiv:2410.22973.
  10. 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., Frequency ratio measurements at 18-digit accuracy using an optical clock network, Nature (London) 591, 564 (2021).
  11. T. E. Mehlstäubler, G. Grosche, C. Lisdat, P. O. Schmidt, and H. Denker, Atomic clocks for geodesy, Rep. Prog. Phys. 81, 064401 (2018).
  12. J. Grotti, I. Nosske, S. 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).
  13. 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).
  14. Y. Yuan, K. Cui, D. Liu, J. Yuan, J. Cao, D. Wang, S. Chao, H. Shu, and X. Huang, Demonstration of chronometric leveling using transportable optical clocks beyond laser coherence limit, Phys. Rev. Appl. 21, 044052 (2024).
  15. R. M. Godun, P. B. R. Nisbet-Jones, J. M. Jones, S. A. King, L. A. M. Johnson, H. S. Margolis, K. Szymaniec, S. N. Lea, K. Bongs, and P. Gill, Frequency ratio of two optical clock transitions in Yb+171 and constraints on the time variation of fundamental constants, Phys. Rev. Lett. 113, 210801 (2014).
  16. M. S. Safronova, The search for variation of fundamental constants with clocks, Ann. Phys. 531, 1800364 (2019).
  17. 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).
  18. M. Filzinger, A. R. Caddell, D. Jani, M. Steinel, L. Giani, N. Huntemann, and B. M. Roberts, Ultralight dark matter search with space-time separated atomic clocks and cavities Phys. Rev. Lett. 134, 031001 (2025).
  19. 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).
  20. 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).
  21. C.-H. Yeh, K. C. Grensemann, L. S. Dreissen, H. A. Fürst, and T. E. Mehlstäubler, Robust and scalable rf spectroscopy in first-order magnetic sensitive states at second-long coherence time, New J. Phys. 25, 093054 (2023).
  22. A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, Optical atomic clocks, Rev. Mod. Phys. 87, 637 (2015).
  23. 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 (1993).
  24. E. Peik, T. Schneider, and C. Tamm, Laser frequency stabilization to a single ion, J. Phys. B: At. Mol. Opt. Phys. 39, 145 (2006).
  25. F. Riehle, Frequency Standards: Basics and Applications (Wiley-VCH, Weinheim, 2004).
  26. K. Pyka, N. Herschbach, J. Keller, and T. E. Mehlstäubler, A high-precision segmented Paul trap with minimized micromotion for an optical multiple-ion clock, Appl. Phys. B 114, 231 (2014).
  27. J. Keller, T. Burgermeister, D. Kalincev, J. Kiethe, and T. E. Mehlstäubler, Evaluation of trap-induced systematic frequency shifts for a multi-ion optical clock at the 10−19 level, J. Phys.: Conf. Ser. 723, 012027 (2016).
  28. T. R. Tan, R. Kaewuam, K. J. Arnold, S. R. Chanu, Z. Zhang, M. S. Safronova, and M. D. Barrett, Suppressing inhomogeneous broadening in a lutetium multi-ion optical clock, Phys. Rev. Lett. 123, 063201 (2019).
  29. L. Pelzer, K. Dietze, V. J. Martínez-Lahuerta, L. Krinner, J. Kramer, F. Dawel, N. C. H. Spethmann, K. Hammerer, and P. O. Schmidt, Multi-ion frequency reference using dynamical decoupling, Phys. Rev. Lett. 133, 033203 (2024).
  30. N. Akerman and R. Ozeri, Operating a multi-ion clock with dynamical decoupling, Phys. Rev. Lett. 134, 013201 (2025).
  31. I. D. Leroux, N. Scharnhorst, S. Hannig, J. Kramer, L. Pelzer, M. Stepanova, and P. O. Schmidt, On-line estimation of local oscillator noise and optimisation of servo parameters in atomic clocks, Metrologia 54, 307 (2017).
  32. D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, 1.5µm lasers with sub-10 mHz linewidth, Phys. Rev. Lett. 118, 263202 (2017).
  33. S. Dörscher, A. Al-Masoudi, M. Bober, R. Schwarz, R. Hobson, U. Sterr, and C. Lisdat, Dynamical decoupling of laser phase noise in compound atomic clocks, Commun. Phys. 3, 185 (2020).
  34. T. Rosenband and D. R. Leibrandt, Exponential scaling of clock stability with atom number, arXiv:1303.6357.
  35. J. Borregaard and A. S. Sørensen, Efficient atomic clocks operated with several atomic ensembles, Phys. Rev. Lett. 111, 090802 (2013).
  36. V. J. Martínez-Lahuerta, S. Eilers, T. E. Mehlstäubler, P. O. Schmidt, and K. Hammerer, Ab initio quantum theory of mass defect and time dilation in trapped-ion optical clocks, Phys. Rev. A 106, 032803 (2022).
  37. M. Brownnutt, M. Kumph, P. Rabl, and R. Blatt, Ion-trap measurements of electric-field noise near surfaces, Rev. Mod. Phys. 87, 1419 (2015).
  38. M. Zeng, Y. Huang, B. Zhang, Y. Hao, Z. Ma, R. Hu, H. Zhang, Z. Chen, M. Wang, H. Guan, and K. Gao, Toward a transportable Ca+ optical clock with a systematic uncertainty of 4.8×10−18, Phys. Rev. Appl. 19, 064004 (2023).
  39. N. Huntemann, C. Sanner, B. Lipphardt, Chr. Tamm, and E. Peik, Single-ion atomic clock with 3×10−18 systematic uncertainty, Phys. Rev. Lett. 116, 063001 (2016).
  40. Z. Y. Ma, K. Deng, Z. Y. Wang, W. Z. Wei, P. Hao, H. X. Zhang, L. R. Pang, B. Wang, F. F. Wu, H. L. Liu, W. H. Yuan, J. L. Chang, J. X. Zhang, Q. Y. Wu, J. Zhang, and Z. H. Lu, Quantum-logic-based Mg+25−Al+27 optical frequency standard for the redefinition of the SI second, Phys. Rev. Appl. 21, 044017 (2024).
  41. T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place, Science 319, 1808 (2008).
  42. Z. Zhiqiang, K. J. Arnold, R. Kaewuam, and M. D. Barrett, Lu+176 clock comparison at the 10−18 level via correlation spectroscopy, Sci. Adv. 9, eadg1971 (2023).
  43. 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).
  44. K. Cui, S. Chao, C. Sun, S. Wang, P. Zhang, Y. Wei, J. Yuan, J. Cao, H. Shu, and X. Huang, Evaluation of the systematic shifts of a Ca+40−Al+27 optical clock, Eur. Phys. J. D 76, 140 (2022).
  45. C. F. Roos, D. Leibfried, A. Mundt, F. Schmidt-Kaler, J. Eschner, and R. Blatt, Experimental demonstration of ground state laser cooling with electromagnetically induced transparency, Phys. Rev. Lett. 85, 5547 (2000).
  46. R. Lechner, C. Maier, C. Hempel, P. Jurcevic, B. P. Lanyon, T. Monz, M. Brownnutt, R. Blatt, and C. F. Roos, Electromagnetically-induced-transparency ground-state cooling of long ion strings, Phys. Rev. A 93, 053401 (2016).
  47. N. Scharnhorst, J. Cerrillo, J. Kramer, I. D. Leroux, J. B. Wübbena, A. Retzker, and P. O. Schmidt, Experimental and theoretical investigation of a multimode cooling scheme using multiple electromagnetically-induced-transparency resonances, Phys. Rev. A 98, 023424 (2018).
  48. C. Sun, K. Cui, S. Chao, Y. Wei, J. Yuan, J. Cao, H. Shu, and X. Huang, Sympathetic electromagnetically induced transparency ground state cooling of a Ca+40–Al+27 pair in an Al+27 clock, Chin. Phys. B 32, 050601 (2023).
  49. J.-S. Chen, S. M. Brewer, C. W. Chou, D. J. Wineland, D. R. Leibrandt, and D. B. Hume, Sympathetic ground state cooling and time-dilation shifts in an Al+27 optical clock, Phys. Rev. Lett. 118, 053002 (2017).
  50. J. A. Kramer, An aluminum optical clock setup and its evaluation using Ca+, Ph.D. thesis, Leibniz Universität Hannover, 2023.
  51. 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).
  52. G. Morigi, J. Eschner, and C. H. Keitel, Ground state laser cooling using electromagnetically induced transparency, Phys. Rev. Lett. 85, 4458 (2000).
  53. D. Hume, T. Rosenband, and D. Wineland, High-fidelity adaptive qubit detection through repetitive quantum nondemolition measurements, Phys. Rev. Lett. 99, 120502 (2007).
  54. S. Amairi, A long optical cavity for sub-hertz laser spectroscopy, Ph.D. thesis, Leibniz Universität Hannover, 2014.
  55. N. Scharnhorst, J. B. Wübbena, S. Hannig, K. Jakobsen, J. Kramer, I. D. Leroux, and P. O. Schmidt, High-bandwidth transfer of phase stability through a fiber frequency comb, Opt. Express 23, 19771 (2015).
  56. E. Benkler, B. Lipphardt, T. Puppe, R. Wilk, F. Rohde, and U. Sterr, End-to-end topology for fiber comb based optical frequency transfer at the 10−21 level, Opt. Express 27, 36886 (2019).
  57. J. Ye, J.-L. Peng, R. J. Jones, K. W. Holman, J. L. Hall, D. J. Jones, S. A. Diddams, J. Kitching, S. Bize, J. C. Bergquist, L. W. Hollberg, L. Robertsson, and L.-S. Ma, Delivery of high-stability optical and microwave frequency standards over an optical fiber network, J. Opt. Soc. Am. B 20, 1459 (2003).
  58. B. Kraus, F. Dawel, S. Hannig, J. Kramer, C. Nauk, and P. O. Schmidt, Phase-stabilized UV light at 267 nm through twofold second harmonic generation, Opt. Express 30, 44992 (2022).
  59. Y. Colombe, D. H. Slichter, A. C. Wilson, D. Leibfried, and D. J. Wineland, Single-mode optical fiber for high-power, low-loss UV transmission, Opt. Express 22, 19783 (2014).
  60. C. D. Marciniak, H. B. Ball, A. T.-H. Hung, and M. J. Biercuk, Towards fully commercial, UV-compatible fiber patch cords, Opt. Express 25, 15643 (2017).
  61. R. Schwarz, A cryogenic strontium lattice clock, Doctoral thesis, Institutionelles Repositorium der Leibniz Universität Hannover, Hannover, 2022.
  62. A. J. Rasmusson, M. D’Onofrio, Y. Xie, J. Cui, and P. Richerme, Optimized pulsed sideband cooling and enhanced thermometry of trapped ions, Phys. Rev. A 104, 043108 (2021).
  63. D. A. Steck, Quantum and Atom Optics, http://steck.us/teaching.
  64. K. D. Bonin and V. V. Kresin, Electric-Dipole Polarizabilities of  Atoms, Molecules, and Clusters (World Scientific, Singapore, 1997).
  65. D. R. Dounas-Frazer, K. Tsigutkin, A. Family, and D. Budker, Measurement of dynamic Stark polarizabilities by analyzing spectral line shapes of forbidden transitions, Phys. Rev. A 82, 062507 (2010).
  66. C. Shi, J.-L. Robyr, U. Eismann, M. Zawada, L. Lorini, R. L. Targat, and J. Lodewyck, Polarizabilities of the Sr87 clock transition, Phys. Rev. A 92, 012516 (2015).
  67. M. Hettrich, T. Ruster, H. Kaufmann, C. F. Roos, C. T. Schmiegelow, F. Schmidt-Kaler, and U. G. Poschinger, Measurement of dipole matrix elements with a single trapped ion, Phys. Rev. Lett. 115, 143003 (2015).
  68. A. Kiruga, C. Cheung, D. Filin, P. Barakhshan, A. Bhosale, V. Badhan, B. Arora, R. Eigenmann, and M. S. Safronova, Portal for high-precision atomic data and computation, arXiv:2506.08170.
  69. Y.-F. Wei, S.-J. Chao, K.-F. Cui, C.-B. Li, S.-C. Yu, H. Zhang, H.-L. Shu, J. Cao, and X.-R. Huang, Improved measurement of the differential polarizability using co-trapped ions, Phys. Rev. Lett. 133, 033001 (2024).
  70. S. Kotler, N. Akerman, Y. Glickman, A. Keselman, and R. Ozeri, Single-ion quantum lock-in amplifier, Nature (London) 473, 61 (2011).
  71. 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).
  72. J. B. Wübbena, S. Amairi, O. Mandel, and P. O. Schmidt, Sympathetic cooling of mixed-species two-ion crystals for precision spectroscopy, Phys. Rev. A 85, 043412 (2012).
  73. 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).
  74. B. Arora, M. S. Safronova, and C. W. Clark, Blackbody‐radiation shift in a 43Ca+ ion optical frequency standard, Phys. Rev. A 76, 064501 (2007).
  75. M. G. Kozlov, S. G. Porsev, and V. V. Flambaum, Manifestation of the nuclear anapole moment in the M1 transitions in bismuth, J. Phys. B: At. Mol. Opt. Phys. 29, 689 (1996).
  76. M. G. Kozlov, S. G. Porsev, M. S. Safronova, and I. I. Tupitsyn, Ci-mbpt: A package of programs for relativistic atomic calculations based on a method combining configuration interaction and many-body perturbation theory, Comput. Phys. Commun. 195, 199 (2015).
  77. V. A. Dzuba, V. V. Flambaum, and M. G. Kozlov, Combination of the many-body perturbation theory with the configuration-interaction method, Phys. Rev. A 54, 3948 (1996).
  78. M. S. Safronova, M. G. Kozlov, W. R. Johnson, and D. Jiang, Development of a configuration-interaction plus all-order method for atomic calculations, Phys. Rev. A 80, 012516 (2009).
  79. V. A. Dzuba, M. G. Kozlov, S. G. Porsev, and V. V. Flambaum, Using effective operators in calculating the hyperfine structure of atoms, J. Exp. Theor. Phys. 87, 885 (1998).
  80. V. A. Dzuba, V. V. Flambaum, P. G. Silvestrov, and O. P. Sushkov, Correlation potential method for the calculation of energy levels, hyperfine structure and E1 transition amplitudes in atoms with one unpaired electron, J. Phys. B 20, 1399 (1987).
  81. S. A. Blundell, W. R. Johnson, Z. W. Liu, and J. Sapirstein, Relativistic all-order calculations of energies and matrix elements for Li and Be+, Phys. Rev. A 40, 2233 (1989).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation