Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

The thorium-229 low-energy isomer and the nuclear clock

Abstract

The 229Th nucleus has an isomeric state at an energy of about 8 eV above the ground state, several orders of magnitude lower than typical nuclear excitation energies. This has inspired the development of a field of low-energy nuclear physics in which nuclear transition rates are influenced by the electron shell. The low energy makes the 229Th isomer accessible to resonant laser excitation. Observed in laser-cooled trapped thorium ions or with thorium dopant ions in a transparent solid, the nuclear resonance may serve as the reference for an optical clock of very high accuracy. Precision frequency comparisons between such a nuclear clock and conventional atomic clocks will provide sensitivity to the effects of hypothetical new physics beyond the standard model. Although laser excitation of 229Th remains an unsolved challenge, recent experiments have provided essential information on the transition energy and relevant nuclear properties, advancing the field.

Key points

  • A nuclear clock, based on a radiative transition in the nucleus, is less sensitive to external perturbations and therefore potentially more precise than established atomic clocks that are based on transitions in the electron shell.

  • The 229Th nucleus is the prime candidate for the realization of a nuclear clock because it possesses a low-energy (8 eV) excited state that is amenable to resonant laser excitation from the nuclear ground state, with an expected natural linewidth in the millihertz range.

  • Recent experiments have provided essential information on the nuclear properties of 229Th (half-life 7,920 years), such as the nuclear moments, decay modes of the isomer and a more precise value of the isomer excitation energy, which is required to achieve laser excitation.

  • Thorium-229 is studied as trapped atomic ions in vacuum or doped into transparent crystals such as CaF2. Because the nuclear transition energy is in the range of transitions of valence electrons, the electronic state may influence the nuclear excitation and decay rates.

  • Because of a fine balance of contributions from the strong and electromagnetic interactions to the nuclear transition energy, a 229Th clock would be sensitive to predicted effects of physics beyond the standard model, such as temporal or spatial variations of fundamental constants.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Section of the table of nuclides showing the natural decay paths leading to the production of (isomeric) 229Th.
Fig. 2: Schematic of the energy levels of 229Th.
Fig. 3: Lineshape of the 29.19-keV doublet.
Fig. 4: Simulated hyperfine structure of the F5/2 → D5/2 electronic transition at 690 nm in 229Th3+ for the nuclear ground state and the isomer.
Fig. 5: Routes to excitation of the nucleus via coupling to the electronic structure.
Fig. 6: Schematics of VUV laser sources for resonant excitation of the 229Th nucleus.

Data availability

The raw data for Fig. 3 are available in the Zenodo repository121.

References

  1. 1.

    Pauli, W. Zur Frage der theoretischen Deutung der Satelliten einiger Spektrallinien und ihrer Beeinflussung durch magnetische Felder. Naturwissenschaften 12, 741–743 (1924).

    ADS  Google Scholar 

  2. 2.

    Casimir, H. Über die hyperfeinstruktur des Europiums. Physica 2, 719–723 (1935).

    ADS  Google Scholar 

  3. 3.

    Rabi, I. I., Zacharias, J. R., Millman, S. & Kusch, P. A new method of measuring nuclear magnetic moment. Phys. Rev. 53, 318 (1938).

    ADS  Google Scholar 

  4. 4.

    Laurence, W. L. Cosmic pendulum for clock planned. New York Times, 34 (21 January 1945).

  5. 5.

    Ramsey, N. F. History of early atomic clocks. Metrologia 42, 1–3 (2005).

    ADS  Google Scholar 

  6. 6.

    Ludlow, A. D., Boyd, M. M., Ye, J., Peik, E. & Schmidt, P. O. Optical atomic clocks. Rev. Mod. Phys. 87, 637 (2015).

    ADS  Google Scholar 

  7. 7.

    Peik, E. & Tamm, C. Nuclear laser spectroscopy of the 3.5 eV transition in Th-229. Europhys. Lett. 61, 181–186 (2003). Proposal of a high-precision optical nuclear clock based on 229Th.

    ADS  Google Scholar 

  8. 8.

    Campbell, C. J. et al. Single-ion nuclear clock for metrology at the 19th decimal place. Phys. Rev. Lett. 108, 120802 (2012). A detailed theoretical analyis of the achievable accuracy of a 229Th nuclear clock with trapped ions.

    ADS  Google Scholar 

  9. 9.

    Kroger, L. A. & Reich, C. W. Features of the low-energy level scheme of 229Th as observed in the α-decay of 233U. Nucl. Phys. A 259, 29–60 (1976).

    ADS  Google Scholar 

  10. 10.

    Peik, E. & Okhapkin, M. Nuclear clocks based on resonant excitation of γ-transitions. C. R. Phys. 16, 516–523 (2015).

    Google Scholar 

  11. 11.

    Thirolf, P. G., Seiferle, B. & von der Wense, L. The 229-thorium isomer: doorway to the road from the atomic clock to the nuclear clock. J. Phys. B 52, 203001 (2019).

    ADS  Google Scholar 

  12. 12.

    Matinyan, S. Lasers as a bridge between atomic and nuclear physics. Phys. Rep. 298, 199–249 (1998).

    ADS  Google Scholar 

  13. 13.

    Tkalya, E. V. Properties of the optical transition in the 229Th nucleus. Phys. Uspekhi 46, 315–320 (2003).

    ADS  Google Scholar 

  14. 14.

    Pálffy, A. Nuclear effects in atomic transitions. Contemp. Phys. 51, 471 (2010).

    ADS  Google Scholar 

  15. 15.

    von der Wense, L., Seiferle, B. & Thirolf, P. G. Towards a 229Th-based nuclear clock. Meas. Tech. 60, 13–22 (2018).

    Google Scholar 

  16. 16.

    Peik, E., Zimmermann, K., Okhapkin, M. & Tamm, C. H. R. Prospects for a nuclear optical frequency standard based on thorium-229. In Proc. 7th Symposium on Frequency Standards and Metrology, ISFSM 2008, 532–538 (World Scientific, 2009).

  17. 17.

    von der Wense, L. & Seiferle, B. The 229Th isomer: prospects for a nuclear optical clock. Eur. Phys. J. A 56, 277 (2020).

    ADS  Google Scholar 

  18. 18.

    Varga, Z., Nicholl, A. & Mayer, K. Determination of the 229Th half-life. Phys. Rev. C 89, 1–6 (2014).

    Google Scholar 

  19. 19.

    Orth, D. A. SRP thorium processing experience. https://www.osti.gov/biblio/6570656 (2020).

  20. 20.

    Forsberg, C. W. & Lewis, L. C. Uses for uranium-233: what should be kept for future needs? ORNL 6952, 7 (1999).

    Google Scholar 

  21. 21.

    Hogle, S. et al. Reactor production of thorium-229. Appl. Radiat. Isot. 114, 19–27 (2016).

    Google Scholar 

  22. 22.

    Egorov, V. N. Hyperfine structure of the atomic spectrum and the nuclear moments of the thorium-229 isotope. Opt. Spectrosc. 16, 549–554 (1964).

    Google Scholar 

  23. 23.

    Gulda, K., et al. The nuclear structure of 229Th. Nucl. Phys. A 703, 45–69 (2002).

    ADS  Google Scholar 

  24. 24.

    Litvinova, E., Feldmeier, H., Dobaczewski, J. & Flambaum, V. Nuclear structure of lowest 229Th states and time-dependent fundamental constants. Phys. Rev. C 79, 064303 (2009).

    ADS  Google Scholar 

  25. 25.

    Thielking, J. et al. Laser spectroscopic characterization of the nuclear-clock isomer 229mTh. Nature 556, 321 (2018). Laser spectroscopic investigation of properties of the 229Th isomer.

    ADS  Google Scholar 

  26. 26.

    Safronova, M. S., Safronova, U. I., Radnaev, A. G., Campbell, C. J. & Kuzmich, A. Magnetic dipole and electric quadrupole moments of the 229Th nucleus. Phys. Rev. A 88, 060501 (2013).

    ADS  Google Scholar 

  27. 27.

    Minkov, N. & Pálffy, A. Reduced transition probabilities for the gamma decay of the 7.8 eV isomer in 229Th. Phys. Rev. Lett. 118, 212501 (2017).

    ADS  Google Scholar 

  28. 28.

    Seiferle, B., von der Wense, L. & Thirolf, P. G. Lifetime measurement of the 229Th nuclear isomer. Phys. Rev. Lett. 118, 042501 (2017).

    ADS  Google Scholar 

  29. 29.

    Sakharov, S. L. On the energy of the 3.5-eV level in 229Th. Phys. At. Nucl. 73, 1–8 (2010).

    Google Scholar 

  30. 30.

    Beck, B. R. et al. Energy splitting of the ground-state doublet in the nucleus 229Th. Phys. Rev. Lett. 98, 142501 (2007). Precise γ-spectroscopy measurement of the isomer energy.

    ADS  Google Scholar 

  31. 31.

    Verlinde, M. et al. Alternative approach to populate and study the 229Th nuclear clock isomer. Phys. Rev. C 100, 24315 (2019).

    ADS  Google Scholar 

  32. 32.

    Kofoed-Hansen, O. On the theory of the recoil in β-decay. Phys. Rev. 74, 1785–1788 (1948).

    ADS  Google Scholar 

  33. 33.

    Ferrer, R. et al. Towards high-resolution laser ionization spectroscopy of the heaviest elements in supersonic gas jet expansion. Nat. Commun. 8, 14520 (2017).

    ADS  Google Scholar 

  34. 34.

    Paul, W. Electromagnetic traps for charged and neutral particles. Rev. Mod. Phys. 62, 531 (1990).

    ADS  Google Scholar 

  35. 35.

    Sanner, C. et al. Optical clock comparison for Lorentz symmetry testing. Nature 567, 204–208 (2019).

    ADS  Google Scholar 

  36. 36.

    Brewer, S. M. et al. 27Al+ quantum-logic clock with a systematic uncertainty below 10−18. Phys. Rev. Lett. 123, 033201 (2019).

    ADS  Google Scholar 

  37. 37.

    Kälber, W. et al. Nuclear radii of thorium isotopes from laser spectroscopy of stored ions. Z. Phys. A 334, 103–108 (1989).

    ADS  Google Scholar 

  38. 38.

    Campbell, C. J., Radnaev, A. G. & Kuzmich, A. Wigner crystals of 229Th for optical excitation of the nuclear isomer. Phys. Rev. Lett. 106, 223001 (2011).

    ADS  Google Scholar 

  39. 39.

    Meier, D.-M. et al. Electronic level structure of Th+ in the range of the 229mTh isomer energy. Phys. Rev. A 99, 52514 (2019).

    ADS  Google Scholar 

  40. 40.

    Groot-Berning, K. et al. Trapping and sympathetic cooling of single thorium ions for spectroscopy. Phys. Rev. A 99, 023420 (2019).

    ADS  Google Scholar 

  41. 41.

    Herrera-Sancho, O. A. et al. Two-photon laser excitation of trapped 232Th+ ions via the 402-nm resonance line. Phys. Rev. A 85, 033402 (2012).

    ADS  Google Scholar 

  42. 42.

    Feiock, F. D. & Johnson, W. R. Atomic susceptibilities and shielding factors. Phys. Rev. 187, 39–50 (1969).

    ADS  Google Scholar 

  43. 43.

    Schmidt, P. O. et al. Spectroscopy using quantum logic. Science 309, 749–752 (2005).

    ADS  Google Scholar 

  44. 44.

    v.d. Wense, L., Seiferle, B., Laatiaoui, M. & Thirolf, P. G. Determination of the extraction efficiency for 233U source α-recoil ions from the MLL buffer-gas stopping cell. Eur. Phys. J. A 51, 29 (2015).

    ADS  Google Scholar 

  45. 45.

    Haas, R. et al. Development of a recoil ion source providing slow Th ions including 229(m)Th in a broad charge state distribution. Hyperfine Interact. 241, 25 (2020).

    ADS  Google Scholar 

  46. 46.

    Gunter, K., Asaro, F. & Helmholz, A. C. Charge and energy distributions of recoils from Th226 alpha decay. Phys. Rev. Lett. 16, 362–364 (1966).

    ADS  Google Scholar 

  47. 47.

    Zimmermann, K., Okhapkin, M. V., Herrera-Sancho, O. A. & Peik, E. Laser ablation loading of a radiofrequency ion trap. Appl. Phys. B Lasers Opt. 107, 883–889 (2012).

    ADS  Google Scholar 

  48. 48.

    Campbell, C. J. et al. Multiply charged thorium crystals for nuclear laser spectroscopy. Phys. Rev. Lett. 102, 233004 (2009).

    ADS  Google Scholar 

  49. 49.

    Jeet, J. et al. Results of a direct search using synchrotron radiation for the low-energy 229Th nuclear isomeric transition. Phys. Rev. Lett. 114, 253001 (2015).

    ADS  Google Scholar 

  50. 50.

    Stellmer, S. et al. Attempt to optically excite the nuclear isomer in 229Th. Phys. Rev. A 97, 062506 (2018).

    ADS  Google Scholar 

  51. 51.

    Jackson, R. A., Amaral, J. B., Valerio, M. E. G., Demille, D. P. & Hudson, E. R. Computer modelling of thorium doping in LiCaAlF6 and LiSrAlF6: application to the development of solid state optical frequency devices. J. Phys. Condens. Matter 21, 325403 (2009).

    Google Scholar 

  52. 52.

    Dessovic, P. et al. 229Thorium-doped calcium fluoride for nuclear laser spectroscopy. J. Phys. Condens. Matter 26, 105402 (2014).

    Google Scholar 

  53. 53.

    Pimon, M. et al. DFT calculation of 229thorium-doped magnesium fluoride for nuclear laser spectroscopy. J. Phys. Condens. Matter 32, 255503 (2020).

    ADS  Google Scholar 

  54. 54.

    Masuda, T. et al. X-ray pumping of the 229Th nuclear clock isomer. Nature 573, 238–242 (2019).

    ADS  Google Scholar 

  55. 55.

    Nickerson, B. S. et al. Nuclear excitation of the 229Th isomer via defect states in doped crystals. Phys. Rev. Lett. 125, 032501 (2020).

    ADS  Google Scholar 

  56. 56.

    Rellergert, W. G. et al. Constraining the evolution of the fundamental constants with a solid-state optical frequency reference based on the 229Th nucleus. Phys. Rev. Lett. 104, 200802 (2010).

    ADS  Google Scholar 

  57. 57.

    Kazakov, G. A. et al. Performance of a 229thorium solid-state nuclear clock. N. J. Phys. 14, 083019 (2012).

    Google Scholar 

  58. 58.

    Nickerson, B. S., Liao, W.-T. & Pálffy, A. Collective effects in 229Th-doped crystals. Phys. Rev. A 98, 062520 (2018).

    ADS  Google Scholar 

  59. 59.

    Zhao, X. et al. Observation of the deexcitation of the 229mTh nuclear isomer. Phys. Rev. Lett. 109, 160801 (2012).

    ADS  Google Scholar 

  60. 60.

    Stellmer, S., Schreitl, M., Kazakov, G. A., Sterba, J. H. & Schumm, T. Feasibility study of measuring the 229Th nuclear isomer transition with 233U-doped crystals. Phys. Rev. C 94, 14302 (2016).

    ADS  Google Scholar 

  61. 61.

    Borisyuk, P. V. et al. Excitation of 229Th nuclei in laser plasma: the energy and half-life of the low-lying isomeric state. Preprint at https://arxiv.org/abs/1804.00299 (2018).

  62. 62.

    Stellmer, S., Schreitl, M. & Schumm, T. Radioluminescence and photoluminescence of Th:CaF2 crystals. Sci. Rep. 5, 15580 (2015).

    ADS  Google Scholar 

  63. 63.

    Reich, C. W., Helmer, R. G., Baker, J. D. & Gehrke, R. J. Emission probabilities and energies of of γ-ray transitions from the decay of 233U. Int. J. Appl. Radiat. Isot. 35, 185–188 (1984).

    Google Scholar 

  64. 64.

    Reich, C. W. & Helmer, R. G. Energy separation of the doublet of intrinsic states at the ground state of 229Th. Phys. Rev. Lett. 64, 271–273 (1990).

    ADS  Google Scholar 

  65. 65.

    Helmer, R. G. & Reich, C. W. An excited state of 229Th at 3.5 eV. Phys. Rev. C 49, 1845–1858 (1994).

    ADS  Google Scholar 

  66. 66.

    Irwin, G. M. & Kim, K. H. Observation of electromagnetic radiation from deexcitation of the 229Th isomer. Phys. Rev. Lett. 79, 990–993 (1997).

    ADS  Google Scholar 

  67. 67.

    Richardson, D. S., Benton, D. M., Evans, D. E., Griffith, J. A. R. & Tungate, G. Ultraviolet photon emission observed in the search for the decay of the 229Th isomer. Phys. Rev. Lett. 80, 3206–3208 (1998).

    ADS  Google Scholar 

  68. 68.

    Shaw, R. W., Young, J. P., Cooper, S. P. & Webb, O. F. Spontaneous ultraviolet emission from 233uranium/229thorium samples. Phys. Rev. Lett. 82, 1109–1111 (1999).

    ADS  Google Scholar 

  69. 69.

    Utter, S. B. et al. Reexamination of the optical gamma ray decay in 229Th. Phys. Rev. Lett. 82, 505–508 (1999).

    ADS  Google Scholar 

  70. 70.

    Guimarães-Filho, Z. O. & Helene, O. Energy of the 3/2+ state of 229Th reexamined. Phys. Rev. C 71, 044303 (2005).

    ADS  Google Scholar 

  71. 71.

    Beck, B. R. et al. Improved Value for the Energy Splitting of the Ground-state Doublet in the Nucleus 229Th. Report No. LLNL-PROC-415170 (Lawrence Livermore National Lab, 2009).

  72. 72.

    Kazakov, G. A., Schumm, T. & Stellmer, S. Re-evaluation of the Beck et al. data to constrain the energy of the Th-229 isomer. Preprint at https://arxiv.org/abs/1702.00749 (2017).

  73. 73.

    Sikorsky, T. et al. Measurement of the 229Th isomer energy with a magnetic micro-calorimeter. Phys. Rev. Lett. 125, 142503 (2020). Currently the most precise γ-spectroscopic measurement of the isomer energy.

    ADS  Google Scholar 

  74. 74.

    von der Wense, L. et al. Direct detection of the 229Th nuclear clock transition. Nature 533, 47–51 (2016). Direct detection of the isomer in recoil ions from the decay of 233U.

    ADS  Google Scholar 

  75. 75.

    Church, E. L. & Weneser, J. Nuclear structure effects in internal conversion. Annu. Rev. Nucl. Sci. 10, 193–234 (1960).

    ADS  Google Scholar 

  76. 76.

    Seiferle, B. et al. Energy of the 229Th nuclear clock transition. Nature 573, 243–246 (2019). Currently the most precise conversion electron measurement of the isomer energy.

    ADS  Google Scholar 

  77. 77.

    von der Wense, L. & Zhang, C. Concepts for direct frequency-comb spectroscopy of 229mTh and an internal-conversion-based solid-state nuclear clock. Eur. Phys. J. D 74, 146 (2020).

    ADS  Google Scholar 

  78. 78.

    Seiferle, B. Characterization of the 229Th Nuclear Clock Transition. PhD thesis, Ludwig-Maximilians Univ. (2019).

  79. 79.

    Gerstenkorn, S. et al. Structures hyperfines du spectre d’étincelle, moment magnétique et quadrupolaire de l’isotope 229 du thorium. J. Phys. 35, 483–495 (1974).

    Google Scholar 

  80. 80.

    Bemis, C. E. et al. Coulomb excitation of states in 229Th. Phys. Scr. 38, 657–663 (1988).

    ADS  Google Scholar 

  81. 81.

    Tkalya, E. V. Proposal for a nuclear gamma-ray laser of optical range. Phys. Rev. Lett. 106, 162501 (2011).

    ADS  Google Scholar 

  82. 82.

    Dykhne, A. M. & Tkalya, E. V. Matrix element of the anomalously low-energy (3.5 ± 0.5 eV) transition in 229Th and the isomer lifetime. JETP Lett. 67, 251–256 (1998).

    ADS  Google Scholar 

  83. 83.

    Minkov, N. & Pálffy, A. Theoretical predictions for the magnetic dipole moment of 229mTh. Phys. Rev. Lett. 122, 162502 (2019).

    ADS  Google Scholar 

  84. 84.

    Hayes, A. C., Friar, J. L. & Möller, P. Splitting sensitivity of the ground and 7.6 eV isomeric states of 229Th. Phys. Rev. C 78, 024311 (2008).

    ADS  Google Scholar 

  85. 85.

    Berengut, J. C., Dzuba, V. A., Flambaum, V. V. & Porsev, S. G. Proposed experimental method to determine α sensitivity of splitting between ground and 7.6 eV isomeric states in 229Th. Phys. Rev. Lett. 102, 210801 (2009).

    ADS  Google Scholar 

  86. 86.

    Porsev, S. G. & Flambaum, V. V. Electronic bridge process in 229Th+. Phys. Rev. A 81, 042516 (2010).

    ADS  Google Scholar 

  87. 87.

    Karpeshin, F. F., Band, I. M. & Trzhaskovskaya, M. B. 3.5-eV isomer of 229mTh: how it can be produced. Nucl. Phys. A 654, 579–596 (1999).

    ADS  Google Scholar 

  88. 88.

    Krutov, V. A. & Fomenko, V. N. Influence of electronic shell on gamma radiation of atomic nuclei. Ann. Phys. 476, 291–302 (1968).

    Google Scholar 

  89. 89.

    Morita, M. Nuclear excitation by electron transition and its application to uranium 235 separation. Prog. Theor. Phys. 49, 1574–1586 (1973).

    ADS  Google Scholar 

  90. 90.

    Izawa, Y. & Yamanaka, C. Production of 235Um by nuclear excitation by electron transition in a laser produced uranium plasma. Phys. Lett. B 88, 59–61 (1979).

    ADS  Google Scholar 

  91. 91.

    Strizhov, V. & Tkalya, E. Decay channel of low-lying isomer state of the 229Th nucleus. Sov. Phys. JETP 72, 387–390 (1991).

    Google Scholar 

  92. 92.

    Herrera-Sancho, O. A., Nemitz, N., Okhapkin, M. V. & Peik, E. Energy levels of Th+ between 7.3 and 8.3 eV. Phys. Rev. A 88, 1–7 (2013).

    Google Scholar 

  93. 93.

    Porsev, S. G., Flambaum, V. V., Peik, E. & Tamm, C. Excitation of the isomeric 229mTh nuclear state via an electronic bridge process in 229Th+. Phys. Rev. Lett. 105, 182501 (2010).

    ADS  Google Scholar 

  94. 94.

    Müller, R. A., Volotka, A. V. & Surzhykov, A. Excitation of the 229Th nucleus via a two-photon electronic transition. Phys. Rev. A 99, 042517 (2019).

    ADS  Google Scholar 

  95. 95.

    Meier, D. M. Electronic level structure investigations in Th+ in the energy range of the 229Th isomer. PhD thesis, Leibniz Univ. (2019).

  96. 96.

    Thielking, J. Hyperfine Studies of Th-229 in its Nuclear Ground and Isomeric State. PhD thesis, Leibniz Univ. (2020).

  97. 97.

    Bilous, P. V. et al. Electronic bridge excitation in highly charged 229Th ions. Phys. Rev. Lett. 124, 192502 (2020).

    ADS  Google Scholar 

  98. 98.

    Bilous, P. V., Minkov, N. & Pálffy, A. Electric quadrupole channel of the 7.8 eV 229Th transition. Phys. Rev. C 97, 044320 (2018).

    ADS  Google Scholar 

  99. 99.

    Yamaguchi, A. et al. Experimental search for the low-energy nuclear transition in 229Th with undulator radiation. N. J. Phys. 17, 053053 (2015).

    Google Scholar 

  100. 100.

    Kang, L., Lin, Z., Liu, F. & Huang, B. Removal of A-site alkali and alkaline earth metal cations in KBe2BO3F2-type layered structures to enhance the deep-ultraviolet nonlinear optical capability. Inorg. Chem. 57, 11146–11156 (2018).

    Google Scholar 

  101. 101.

    Kanai, T. et al. Generation of vacuum-ultraviolet light below 160 nm in a KBBF crystal by the fifth harmonic of a single-mode Ti:sapphire laser. J. Opt. Soc. Am. B 21, 370 (2004).

    ADS  Google Scholar 

  102. 102.

    Nakazato, T. et al. Phase-matched frequency conversion below 150 nm in KBe2BO3F2. Opt. Express 24, 17149 (2016).

    ADS  Google Scholar 

  103. 103.

    Bjorklund, G. C. Effects of focusing on third-order nonlinear processes in isotropic media. IEEE J. Quantum Electron. 11, 287–296 (1975).

    ADS  Google Scholar 

  104. 104.

    Hilbig, R., Hilber, G., Lago, A., Wolff, B. & Wallenstein, R. Tunable coherent VUV radiation generated by nonlinear optical frequency conversion in gases. Proc. SPIE 0613, https://doi.org/10.1117/12.960383 (1986).

  105. 105.

    Hanna, S. J. et al. A new broadly tunable (7.4–10.2 eV) laser based VUV light source and its first application to aerosol mass spectrometry. Int. J. Mass. Spectrom. 279, 134–146 (2009).

    Google Scholar 

  106. 106.

    Gohle, C. et al. A frequency comb in the extreme ultraviolet. Nature 436, 234–237 (2005).

    ADS  Google Scholar 

  107. 107.

    Jones, R. J., Moll, K. D., Thorpe, M. J. & Ye, J. Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity. Phys. Rev. Lett. 94, 193201 (2005).

    ADS  Google Scholar 

  108. 108.

    Witte, S., Zinkstok, R. T., Ubachs, W., Hogervorst, W. & Eikema, K. S. E. Deep-ultraviolet quantum interference metrology with ultrashort laser pulses. Science 307, 400–403 (2005).

    ADS  Google Scholar 

  109. 109.

    Yost, D. C. et al. Vacuum-ultraviolet frequency combs from below-threshold harmonics. Nat. Phys. 5, 815–820 (2009).

    Google Scholar 

  110. 110.

    Seres, J. et al. All-solid-state VUV frequency comb at 160 nm using high-harmonic generation in nonlinear femtosecond enhancement cavity. Opt. Express 27, 6618–6628 (2019).

    ADS  Google Scholar 

  111. 111.

    Cingöz, A. et al. Direct frequency comb spectroscopy in the extreme ultraviolet. Nature 482, 68–71 (2012).

    ADS  Google Scholar 

  112. 112.

    Ozawa, A. & Kobayashi, Y. VUV frequency-comb spectroscopy of atomic xenon. Phys. Rev. A 87, 022507 (2013).

    ADS  Google Scholar 

  113. 113.

    Hilborn, R. C. Einstein coefficients, cross sections, f values, dipole moments, and all that. Am. J. Phys. 50, 982–986 (1982).

    ADS  Google Scholar 

  114. 114.

    Cohen-Tannoudji, C. & Guéry-Odelin, D. Advances in Atomic Physics: An Overview (World Scientific, 2011).

  115. 115.

    Safronova, M. S. et al. Search for new physics with atoms and molecules. Rev. Mod. Phys. 90, 025008 (2018).

    MathSciNet  ADS  Google Scholar 

  116. 116.

    Fadeev, P., Berengut, J. C. & Flambaum, V. V. Sensitivity of 229Th nuclear clock transition to variation of the fine-structure constant. Phys. Rev. A 102, 052833 (2020).

    ADS  Google Scholar 

  117. 117.

    Flambaum, V. V. Enhanced effect of temporal variation of the fine structure constant and the strong interaction in 229Th. Phys. Rev. Lett. 97, 092502 (2006). Prediction of the unusually high sensitivity of a 229Th clock in a search for variations of fundamental constants.

    ADS  Google Scholar 

  118. 118.

    Flambaum, V. V. & Wiringa, R. B. Enhanced effect of quark mass variation in 229Th and limits from Oklo data. Phys. Rev. C 79, 034301 (2009).

    ADS  Google Scholar 

  119. 119.

    Stadnik, Y. V. & Flambaum, V. V. Can dark matter induce cosmological evolution of the fundamental constants of nature? Phys. Rev. Lett. 115, 201301 (2015).

    ADS  Google Scholar 

  120. 120.

    Flambaum, V. V. Enhancing the effect of Lorentz invariance and Einstein’s equivalence principle violation in nuclei and atoms. Phys. Rev. Lett. 117, 072501 (2016).

    ADS  Google Scholar 

  121. 121.

    Magnetic micro-calorimeter raw data. https://zenodo.org/record/3931904#.X5WqQYj7SUl (Zenodo, 2020).

Download references

Acknowledgements

Our work on 229Th was supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 664732 “nuClock”, grant agreement no. 856415 “ThoriumNuclearClock” and grant agreement no. 882708 “CrystalClock”. The team has also received funding from the EMPIR project “CC4C”. This project has received funding from the EMPIR programme co-financed by the Participating States and from the European Unions Horizon 2020 research and innovation programme.

Author information

Affiliations

Authors

Contributions

The authors contributed equally to all aspects of the article.

Corresponding author

Correspondence to Ekkehard Peik.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information

Nature Reviews Physics thanks Victor Flambaum, David Leibrandt and the other, anonymous, reviewer for their contribution to the peer review of this work.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Glossary

Sternheimer antishielding

An external electric field gradient may be strongly enhanced at the position of the nucleus by the influence of the deformed electron shell, especially in heavy atoms.

Mössbauer spectroscopy

High-resolution, recoil-free gamma-ray spectroscopy performed with nuclei in solids, tuned via the Doppler shift between a moving source and stationary absorber.

Lamb–Dicke regime

When the motion of an absorber or emitter is constrained to a region that is smaller than the wavelength, the spectrum contains a resonance that is free from the first-order Doppler shift.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Beeks, K., Sikorsky, T., Schumm, T. et al. The thorium-229 low-energy isomer and the nuclear clock. Nat Rev Phys 3, 238–248 (2021). https://doi.org/10.1038/s42254-021-00286-6

Download citation

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing