- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

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

Probing new forces with nuclear clocks

Cédric Delaunay1,*, Seung J. Lee2,†, Roee Ozeri3,‡, Gilad Perez4,§, Wolfram Ratzinger4,∥, and Bingrong Yu5,2,¶

  • *Contact author: cedric.delaunay@lapth.cnrs.fr
  • †Contact author: sjjlee@kias.re.kr
  • ‡Contact author: Roee.Ozeri@weizmann.ac.il
  • §Contact author: gilad.perez@weizmann.ac.il
  • ∥Contact author: wolfram.ratzinger@weizmann.ac.il
  • Contact author: bingrong.yu@cornell.edu
PDF

Phys. Rev. D 112, 095030 – Published 21 November, 2025

DOI: https://doi.org/10.1103/gw1d-hbxj

Abstract

Clocks based on nuclear isomer transitions promise exceptional stability and precision. The low transition energy of the thorium-229 isomer makes it an ideal candidate, as it has been excited by a vacuum-ultraviolet laser and is highly sensitive to subtle interactions. This enables the development of powerful tools for probing new forces, which we call quintessometers. In this work, we demonstrate the potential of nuclear clocks, particularly solid-state variants, to surpass existing limits on scalar field couplings, exceeding the sensitivity of current fifth-force searches at submicron distances and significantly improving equivalence-principle tests at kilometer scales and beyond. Additionally, we highlight the capability of transportable nuclear clocks to detect scalar interactions at distances beyond 10 km, complementing space-based missions.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (84)

  1. P. G. Thirolf, S. Kraemer, D. Moritz, and K. Scharl, The thorium isomer Th229m: Review of status and perspectives after more than 50 years of research, Eur. Phys. J. Spec. Top. 233, 1113 (2024).
  2. B. Seiferle et al., Energy of the Th229 nuclear clock transition, Nature (London) 573, 243 (2019).
  3. C. J. Campbell, A. G. Radnaev, A. Kuzmich, V. A. Dzuba, V. V. Flambaum, and A. Derevianko, A single-ion nuclear clock for metrology at the 19th decimal place, Phys. Rev. Lett. 108, 120802 (2012).
  4. G. A. Kazakov et al., Performance of a Thorium229 solid-state nuclear clock, New J. Phys. 14, 083019 (2012).
  5. R. G. Helmer and C. W. Reich, An excited state of Th-229 at 3.5 eV, Phys. Rev. C 49, 1845 (1994).
  6. S. G. Matinyan, Lasers as a bridge between atomic and nuclear physics, Phys. Rep. 298, 199 (1998).
  7. T. Sikorsky et al., Measurement of the Th229 isomer energy with a magnetic micro-calorimeter, Phys. Rev. Lett. 125, 142503 (2020).
  8. S. Kraemer et al., Observation of the radiative decay of the Th229 nuclear clock isomer, Nature (London) 617, 706 (2023).
  9. J. Tiedau et al., Laser excitation of the Th-229 nucleus, Phys. Rev. Lett. 132, 182501 (2024).
  10. R. Elwell, C. Schneider, J. Jeet, J.  E.  S. Terhune, H.  W.  T. Morgan, A.  N. Alexandrova, H.  B. Tran Tan, A. Derevianko, and E. R. Hudson, Laser excitation of the Th229 nuclear isomeric transition in a solid-state host, Phys. Rev. Lett. 133, 013201 (2024).
  11. C. Zhang et al., Frequency ratio of the Th229m nuclear isomeric transition and the Sr87 atomic clock, Nature (London) 633, 63 (2024).
  12. V. V. Flambaum, Enhanced effect of temporal variation of the fine structure constant and the strong interaction in Th-229, Phys. Rev. Lett. 97, 092502 (2006).
  13. P. Fadeev, J. C. Berengut, and V. V. Flambaum, Sensitivity of Th229 nuclear clock transition to variation of the fine-structure constant, Phys. Rev. A 102, 052833 (2020).
  14. N. Minkov and A. Pálffy, Th229m isomer from a nuclear model perspective, Phys. Rev. C 103, 014313 (2021).
  15. P. Fadeev, J. C. Berengut, and V. V. Flambaum, Effects of variation of the fine structure constant α and quark mass mq in Mössbauer nuclear transitions, Phys. Rev. C 105, L051303 (2022).
  16. A. Caputo et al., Sensitivity of nuclear clocks to new physics, Phys. Rev. C 112, L031302 (2025).
  17. K. Beeks et al., Fine-structure constant sensitivity of the Th-229 nuclear clock transition, Nat. Commun. 16, 9147 (2025).
  18. N. Minkov, A. Pálffy, P. Quentin, and L. Bonneau, Skyrme-Hartree-Fock-BCS approach to Th229m and neighboring nuclei, Phys. Rev. C 110, 034327 (2024).
  19. A. Arvanitaki, J. Huang, and K. Van Tilburg, Searching for dilaton dark matter with atomic clocks, Phys. Rev. D 91, 015015 (2015).
  20. Y. V. Stadnik and V. V. Flambaum, Can dark matter induce cosmological evolution of the fundamental constants of Nature?, Phys. Rev. Lett. 115, 201301 (2015).
  21. M. S. Safronova, D. Budker, D. DeMille, D. F. J. Kimball, A. Derevianko, and C. W. Clark, Search for new physics with atoms and molecules, Rev. Mod. Phys. 90, 025008 (2018).
  22. E. Fuchs, F. Kirk, E. Madge, C. Paranjape, E. Peik, G. Perez, W. Ratzinger, and J. Tiedau, Searching for dark matter with the Th229 nuclear lineshape from laser spectroscopy, Phys. Rev. X 15, 021055 (2025).
  23. H. Kim and G. Perez, Oscillations of atomic energy levels induced by QCD axion dark matter, Phys. Rev. D 109, 015005 (2024).
  24. A. Banerjee, D. Budker, J. Eby, H. Kim, and G. Perez, Relaxion stars and their detection via atomic physics, Commun. Phy. 3, 1 (2020).
  25. A. Banerjee, D. Budker, J. Eby, V. V. Flambaum, H. Kim, O. Matsedonskyi, and G. Perez, Searching for earth/solar axion halos, J. High Energy Phys. 09 (2020) 004.
  26. D. Budker, J. Eby, M. Gorghetto, M. Jiang, and G. Perez, A generic formation mechanism of ultralight dark matter solar halos, J. Cosmol. Astropart. Phys. 12 (2023) 021.
  27. A. Derevianko and M. Pospelov, Hunting for topological dark matter with atomic clocks, Nat. Phys. 10, 933 (2014).
  28. T. Damour, Equivalence principle and clocks, in Proceedings of the 34th Rencontres de Moriond: Gravitational Waves and Experimental Gravity (1999), pp. 357–365, arXiV:gr-qc/9904032.
  29. T. Damour and J. F. Donoghue, Equivalence principle violations and couplings of a light dilaton, Phys. Rev. D 82, 084033 (2010).
  30. R. Oswald et al., Search for dark-matter-induced oscillations of fundamental constants using molecular spectroscopy, Phys. Rev. Lett. 129, 031302 (2022).
  31. A. Banerjee, G. Perez, M. Safronova, I. Savoray, and A. Shalit, The phenomenology of quadratically coupled ultra light dark matter, J. High Energy Phys. 10 (2023) 042.
  32. Aristotle, On the Heavens (W. K. C. Guthrie, Trans.) (Harvard University Press, 1939), ISBN-[Amazon][WorldCat], Original work published ca. 350 BCE.
  33. R. Spero, J. K. Hoskins, R. Newman, J. Pellam, and J. Schultz, Test of the gravitational inverse-square law at laboratory distances, Phys. Rev. Lett. 44, 1645 (1980).
  34. V. M. Mostepanenko and I. Y. Sokolov, Stronger restrictions on the constants of long range forces decreasing as r−n, Phys. Lett. 146A, 373 (1990).
  35. M. Bordag, V. M. Mostepanenko, and I. Y. Sokolov, On the strengthening of restrictions on hypothetical Yukawa type forces with extremely small range of action, Phys. Lett. A 187, 35 (1994).
  36. S. K. Lamoreaux, Demonstration of the Casimir force in the 0.6 to 6 micrometers range, Phys. Rev. Lett. 78, 5 (1997); 81, 5475(E) (1998).
  37. M. Bordag, B. Geyer, G. L. Klimchitskaya, and V. M. Mostepanenko, Constraints for hypothetical interactions from a recent demonstration of the Casimir force and some possible improvements, Phys. Rev. D 58, 075003 (1998).
  38. T. Ederth, Template-stripped gold surfaces with 0.4-nm rms roughness suitable for force measurements: Application to the Casimir force in the 20-100-nm range, Phys. Rev. A 62, 062104 (2000).
  39. B. W. Harris, F. Chen, and U. Mohideen, Precision measurement of the Casimir force using gold surfaces, Phys. Rev. A 62, 052109 (2000).
  40. E. Fischbach, D. E. Krause, V. M. Mostepanenko, and M. Novello, New constraints on ultrashort ranged Yukawa interactions from atomic force microscopy, Phys. Rev. D 64, 075010 (2001).
  41. J. Chiaverini, S. J. Smullin, A. A. Geraci, D. M. Weld, and A. Kapitulnik, New experimental constraints on nonNewtonian forces below 100 microns, Phys. Rev. Lett. 90, 151101 (2003).
  42. E. G. Adelberger, B. R. Heckel, and A. E. Nelson, Tests of the gravitational inverse square law, Annu. Rev. Nucl. Part. Sci. 53, 77 (2003).
  43. J. C. Long, H. W. Chan, A. B. Churnside, E. A. Gulbis, M. C. M. Varney, and J. C. Price, Upper limits to submillimeter-range forces from extra space-time dimensions, Nature (London) 421, 922 (2003).
  44. D. J. Kapner, T. S. Cook, E. G. Adelberger, J. H. Gundlach, B. R. Heckel, C. D. Hoyle, and H. E. Swanson, Tests of the gravitational inverse-square law below the dark-energy length scale, Phys. Rev. Lett. 98, 021101 (2007).
  45. S.-Q. Yang, B.-F. Zhan, Q.-L. Wang, C.-G. Shao, L.-C. Tu, W.-H. Tan, and J. Luo et al., Test of the gravitational inverse square law at millimeter ranges, Phys. Rev. Lett. 108, 081101 (2012).
  46. Y. J. Chen, W.  K. Tham, D.  E. Krause, D. López, E. Fischbach, and R.  S. Decca, Stronger limits on hypothetical Yukawa interactions in the 30–8000 nm range, Phys. Rev. Lett. 116, 221102 (2016).
  47. N. Leefer, A. Gerhardus, D. Budker, V. V. Flambaum, and Y. V. Stadnik, Search for the effect of massive bodies on atomic spectra and constraints on Yukawa-type interactions of scalar particles, Phys. Rev. Lett. 117, 271601 (2016).
  48. W.-H. Tan et al., Improvement for testing the gravitational inverse-square law at the submillimeter range, Phys. Rev. Lett. 124, 051301 (2020).
  49. J. G. Lee, E. G. Adelberger, T. S. Cook, S. M. Fleischer, and B. R. Heckel, New test of the gravitational 1/r2 law at separations down to 52  μm, Phys. Rev. Lett. 124, 101101 (2020).
  50. D. Brzeminski, Z. Chacko, A. Dev, I. Flood, and A. Hook, Searching for a fifth force with atomic and nuclear clocks, Phys. Rev. D 106, 095031 (2022).
  51. S. Schlamminger, K. Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger, Test of the equivalence principle using a rotating torsion balance, Phys. Rev. Lett. 100, 041101 (2008).
  52. G. L. Smith et al., Short range tests of the equivalence principle, Phys. Rev. D 61, 022001 (2000).
  53. J. Bergé, P. Brax, G. Métris, M. Pernot-Borràs, P. Touboul, and J.-P. Uzan, MICROSCOPE mission: First constraints on the violation of the weak equivalence principle by a light scalar dilaton, Phys. Rev. Lett. 120, 141101 (2018).
  54. H. Kim, A. Lenoci, G. Perez, and W. Ratzinger, Probing an ultralight QCD axion with electromagnetic quadratic interaction, Phys. Rev. D 109, 015030 (2024).
  55. A. Derevianko, K. Gibble, L. Hollberg, N. R. Newbury, C. Oates, M. S .Safronova, L. C. Sinclair, and N. Yu, Fundamental physics with a state-of-the-art optical clock in space, Quantum Sci. Technol. 7, 044002 (2022).
  56. MICROSCOPE Collaboration, MICROSCOPE mission: Final results of the test of the equivalence principle, Phys. Rev. Lett. 129, 121102 (2022).
  57. J. Grotti et al., Geodesy and metrology with a transportable optical clock, Nat. Phys. 14, 437 (2018).
  58. M. Bordag, U. Mohideen, and V. M. Mostepanenko, New developments in the Casimir effect, Phys. Rep. 353, 1 (2001).
  59. V. V. Nesvizhevsky, G. Pignol, and K. V. Protasov, Neutron scattering and extra short range interactions, Phys. Rev. D 77, 034020 (2008).
  60. T. Ooi et al., Frequency reproducibility of solid-state Th-229 nuclear clocks, arXiv:2507.01180.
  61. G. Gratta, D. E. Kaplan, and S. Rajendran, Searching for new interactions at sub-micron scale using the Mossbauer effect, Phys. Rev. D 102, 115031 (2020).
  62. H. B. G. Casimir, On the attraction between two perfectly conducting plates, Indagat. Math 10, 261 (1948).
  63. R. S. Decca, D. López, H. B. Chan, E. Fischbach, D. E. Krause, and C. R. Jamell, Constraining new forces in the Casimir regime using the isoelectronic technique, Phys. Rev. Lett. 94, 240401 (2005).
  64. R. Matloob and H. Falinejad, Casimir force between two dielectric slabs, Phys. Rev. A 64, 042102 (2001).
  65. M. P. Hehlen, R. R. Greco, W. G. Rellergert, S. T. Sullivan, D. DeMille, R. A. Jackson, E. R. Hudson, and J. R. Torgerson, Optical spectroscopy of an atomic nucleus: Progress toward direct observation of the Th229 isomer transition, J. Lumin. 133, 91 (2013).
  66. K. Beeks et al., Growth and characterization of thorium-doped calcium fluoride single crystals, Sci. Rep. 13, 3897 (2023).
  67. C. Zhang et al., Th229F4 thin films for solid-state nuclear clocks, Nature (London) 636, 603 (2024).
  68. P. Dessovic, P. Mohn, R. A. Jackson, G. Winkler, M. Schreitl, G. Kazakov, and T. Schumm, Thorium229-doped calcium fluoride for nuclear laser spectroscopy, J. Phys. Condens. Matter 26, 105402 (2014).
  69. V. A. Dzuba and V. V. Flambaum, Effects of electrons on nuclear clock transition frequency in Th229 ions, Phys. Rev. Lett. 131, 263002 (2023).
  70. F. Gebert, Y. Wan, F. Wolf, C. N. Angstmann, J. C. Berengut, and P. O. Schmidt, Precision isotope shift measurements in calcium ions using quantum logic detection schemes, Phys. Rev. Lett. 115, 053003 (2015).
  71. Q. Gong, S. Tao, C. Zhao, Y. Hang, S. Zhu, and L. Ma, Structures and properties of high-concentration doped Th:CaF2 single crystals for solid-state nuclear clock materials, Inorg. Chem. 63, 3807 (2024).
  72. H. de Waard and G. J. Perlow, Mössbauer effect of the 93-keV transition in Zn67, Phys. Rev. Lett. 24, 566 (1970).
  73. H. J. Lipkin, Some simple features of the Mössbauer effect. III: The f-factor for an impurity source in a crystal, Ann. Phys. (N.Y.) 23, 28 (1963).
  74. D. R. Huffman and M. H. Norwood, Specific heat and elastic constants of calcium fluoride at low temperatures, Phys. Rev. 117, 709 (1960).
  75. V. S. Kogan, Isotope effects in the structural properties of solids, Sov. Phys. Usp. 5, 951 (1963).
  76. K. Nalikowski, V. Veryazov, K. Beeks, T. Schumm, and M. Krośnicki, Embedded cluster approach for accurate electronic structure calculations of Th229:CaF2, Phys. Rev. B 111, 115103 (2025).
  77. K. Beeks et al., Optical transmission enhancement of ionic crystals via superionic fluoride transfer: Growing VUV-transparent radioactive crystals, Phys. Rev. B 109, 094111 (2024).
  78. T. Hiraki et al., Laser Mössbauer spectroscopy of Th229, arXiv:2509.00041.
  79. D. A. Shirley, Application and interpretation of isomer shifts, Rev. Mod. Phys. 36, 339 (1964).
  80. V. Chechersky, A. Nath, I. Isaac, J. P. Franck, K. Ghosh, and R. L. Greene, Origin of the giant oxygen-isotope effect in the manganite La0.8Ca0.2MnO3, Phys. Rev. B 60, 3005 (1999).
  81. W. Potzel, Recent Zn67-experiments, Hyperfine Interact. 40, 171 (1988).
  82. A. Banerjee, Probing (ultra-) light dark matter using synchrotron based Mössbauer spectroscopy, arXiv:2408.04700.
  83. T. Katila, K. J. Riski, and J. Ylä-Jääski, Precision determination of the isomer shift of ZN-67 in ZNO, J. Phys. Colloques 41, C1-121 (1980).
  84. J. S. Higgins, T. Ooi, J. F. Doyle, C. Zhang, J. Ye, K. Beeks, T. Sikorsky, and T. Schumm, Temperature sensitivity of a thorium-229 solid-state nuclear clock, Phys. Rev. Lett. 134, 113801 (2025).

Outline

Information

Phys. Rev. D 112, 095030– Published 21 November, 2025
  • Received 13 May 2025
  • Accepted 21 October 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation