{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T19:32:05Z","timestamp":1791487925095,"version":"4.3.4"},"reference-count":69,"publisher":"Springer Science and Business Media LLC","license":[{"start":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T00:00:00Z","timestamp":1791331200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T00:00:00Z","timestamp":1791331200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nature"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    The laser-accessible nuclear transition in the thorium-229 isotope has been identified as a candidate for realizing an optical nuclear clock\n                    <jats:sup>1<\/jats:sup>\n                    that might outperform current optical clocks based on electron-shell transitions in atoms or ions\n                    <jats:sup>2<\/jats:sup>\n                    . It is expected to be more robust against external perturbations\n                    <jats:sup>3,4<\/jats:sup>\n                    and to provide enhanced sensitivity in clock-based tests of the fundamental principles of physics\n                    <jats:sup>5,6<\/jats:sup>\n                    . Here we realize a thorium-229 nuclear clock by stabilizing a continuous-wave laser to the 148-nm nuclear transition with rapid feedback based on absorption spectroscopy\n                    <jats:sup>7<\/jats:sup>\n                    . The thorium-229 nuclei are embedded in a millimetre-sized, room-temperature calcium fluoride crystal. A subharmonic of the 148-nm radiation is continuously compared with a Yb\n                    <jats:sup>+<\/jats:sup>\n                    single-ion clock. The nuclear clock shows a shot-noise-limited fractional frequency instability of\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$3\\times 1{0}^{-12}\/\\sqrt{\\tau \/{\\rm{s}}}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mn>3<\/mml:mn>\n                          <mml:mo>\u00d7<\/mml:mo>\n                          <mml:mn>1<\/mml:mn>\n                          <mml:msup>\n                            <mml:mn>0<\/mml:mn>\n                            <mml:mrow>\n                              <mml:mo>\u2212<\/mml:mo>\n                              <mml:mn>12<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                          <mml:mo>\/<\/mml:mo>\n                          <mml:msqrt>\n                            <mml:mi>\u03c4<\/mml:mi>\n                            <mml:mo>\/<\/mml:mo>\n                            <mml:mi>s<\/mml:mi>\n                          <\/mml:msqrt>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    where\n                    <jats:italic>\u03c4<\/jats:italic>\n                    is the averaging time, approaching 10\n                    <jats:sup>\u221215<\/jats:sup>\n                    instabilities over 1\u2009day of operation. Improvements to the instability by several orders of magnitude are projected for future devices. We use the nuclear clock to constrain models of ultralight dark matter by searching for periodic fluctuations and slow drifts in the nuclear transition energy, on timescales between 20\u2009s and 1\u2009day. Benefitting from the enhanced sensitivity of the thorium-229 transition, these constraints compete with the best atomic clocks concerning dark matter coupling to photons and go beyond previous measurements regarding coupling to the strong force.\n                  <\/jats:p>","DOI":"10.1038\/s41586-026-11084-4","type":"journal-article","created":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T15:03:20Z","timestamp":1791385400000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A thorium-229 optical nuclear clock with feedback loop"],"prefix":"10.1038","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-1907-0688","authenticated-orcid":false,"given":"L.","family":"Toscani De Col","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T.","family":"Riebner","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-4071-7749","authenticated-orcid":false,"given":"I.","family":"Morawetz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-6522-5788","authenticated-orcid":false,"given":"F.","family":"Schneider","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-7822-9627","authenticated-orcid":false,"given":"N.","family":"Sempelmann","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J.","family":"Schlachet-L\u00e9pinay","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7154-0440","authenticated-orcid":false,"given":"F.","family":"Schaden","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-7610-9122","authenticated-orcid":false,"given":"M.","family":"Bartokos","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4110-2380","authenticated-orcid":false,"given":"G. A.","family":"Kazakov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8707-6723","authenticated-orcid":false,"given":"K.","family":"Beeks","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-6550-1601","authenticated-orcid":false,"given":"B.","family":"Gerstenecker","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7784-463X","authenticated-orcid":false,"given":"M.","family":"Pimon","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S.","family":"Lahs","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Hellerschmied","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T.","family":"Lercher","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9112-1729","authenticated-orcid":false,"given":"H.","family":"Denker","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-6127-0577","authenticated-orcid":false,"given":"J.","family":"Premper","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Niessner","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7891-1096","authenticated-orcid":false,"given":"M.","family":"Matus","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6938-3423","authenticated-orcid":false,"given":"M.","family":"\u010c\u00ed\u017eek","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"O.","family":"\u010c\u00edp","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-1428-9814","authenticated-orcid":false,"given":"V.","family":"Lal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9580-8058","authenticated-orcid":false,"given":"G.","family":"Zitzer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"V.","family":"Petrov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2207-230X","authenticated-orcid":false,"given":"J.","family":"Tiedau","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0420-3115","authenticated-orcid":false,"given":"M. V.","family":"Okhapkin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6309-2975","authenticated-orcid":false,"given":"E.","family":"Peik","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1066-202X","authenticated-orcid":false,"given":"T.","family":"Schumm","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,10,7]]},"reference":[{"key":"11084_CR1","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1209\/epl\/i2003-00210-x","volume":"61","author":"E Peik","year":"2003","unstructured":"Peik, E. & Tamm, C. Nuclear laser spectroscopy of the 3.5\u2009eV transition in Th-229. Europhys. Lett. 61, 181 https:\/\/doi.org\/10.1209\/epl\/i2003-00210-x (2003).","journal-title":"Europhys. Lett."},{"key":"11084_CR2","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1103\/RevModPhys.87.637","volume":"87","author":"AD Ludlow","year":"2015","unstructured":"Ludlow, A. D., Boyd, M. M., Ye, J., Peik, E. & Schmidt, P. O. Optical atomic clocks. Rev. Mod. Phys. 87, 637 https:\/\/doi.org\/10.1103\/RevModPhys.87.637 (2015).","journal-title":"Rev. Mod. Phys."},{"key":"11084_CR3","doi-asserted-by":"publisher","first-page":"200802","DOI":"10.1103\/PhysRevLett.104.200802","volume":"104","author":"WG Rellergert","year":"2010","unstructured":"Rellergert, W. G. et al. Constraining the evolution of the fundamental constants with a solid-state optical frequency reference based on the Th 229 nucleus. Phys. Rev. Lett. 104, 200802 https:\/\/doi.org\/10.1103\/PhysRevLett.104.200802 (2010).","journal-title":"Phys. Rev. Lett."},{"key":"11084_CR4","doi-asserted-by":"publisher","first-page":"083019","DOI":"10.1088\/1367-2630\/14\/8\/083019","volume":"14","author":"G Kazakov","year":"2012","unstructured":"Kazakov, G. et al. Performance of a 229thorium solid-state nuclear clock. New J. Phys. 14, 083019 https:\/\/doi.org\/10.1088\/1367-2630\/14\/8\/083019 (2012).","journal-title":"New J. Phys."},{"key":"11084_CR5","doi-asserted-by":"publisher","first-page":"92502","DOI":"10.1103\/PhysRevLett.97.092502","volume":"97","author":"VV Flambaum","year":"2006","unstructured":"Flambaum, V. V. Enhanced effect of temporal variation of the fine structure constant and the strong interaction in 229Th. Phys. Rev. Lett. 97, 92502 https:\/\/doi.org\/10.1103\/PhysRevLett.97.092502 (2006).","journal-title":"Phys. Rev. Lett."},{"key":"11084_CR6","doi-asserted-by":"publisher","first-page":"034002","DOI":"10.1088\/2058-9565\/abe9c2","volume":"6","author":"E Peik","year":"2021","unstructured":"Peik, E. et al. Nuclear clocks for testing fundamental physics. Quantum Sci. Technol. 6, 034002 https:\/\/doi.org\/10.1088\/2058-9565\/abe9c2 (2021).","journal-title":"Quantum Sci. Technol."},{"key":"11084_CR7","doi-asserted-by":"publisher","unstructured":"Morawetz, I. et al. Continuous-wave laser absorption spectroscopy of the thorium-229 nucleus. Nature 657, 626\u2013631 https:\/\/doi.org\/10.1038\/s41586-026-11011-7 (2026).","DOI":"10.1038\/s41586-026-11011-7"},{"key":"11084_CR8","doi-asserted-by":"publisher","first-page":"S31","DOI":"10.1088\/0026-1394\/42\/3\/S05","volume":"42","author":"J Vanier","year":"2005","unstructured":"Vanier, J. & Audoin, C. The classical caesium beam frequency standard: fifty years later. Metrologia 42, S31 https:\/\/doi.org\/10.1088\/0026-1394\/42\/3\/S05 (2005).","journal-title":"Metrologia"},{"key":"11084_CR9","doi-asserted-by":"publisher","first-page":"S64","DOI":"10.1088\/0026-1394\/42\/3\/S08","volume":"42","author":"R Wynands","year":"2005","unstructured":"Wynands, R. & Weyers, S. Atomic fountain clocks. Metrologia 42, S64 https:\/\/doi.org\/10.1088\/0026-1394\/42\/3\/S08 (2005).","journal-title":"Metrologia"},{"key":"11084_CR10","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1364\/OPTICA.575770","volume":"13","author":"TM Fortier","year":"2026","unstructured":"Fortier, T. M., Luiten, A. N. & Margolis, H. S. Optical atomic clocks: defining the future of time and frequency metrology. Optica 13, 143\u2013163 https:\/\/doi.org\/10.1364\/OPTICA.575770 (2026).","journal-title":"Optica"},{"key":"11084_CR11","doi-asserted-by":"publisher","first-page":"120802","DOI":"10.1103\/PhysRevLett.108.120802","volume":"108","author":"CJ Campbell","year":"2012","unstructured":"Campbell, C. J. et al. Single-ion nuclear clock for metrology at the 19th decimal place. Phys. Rev. Lett. 108, 120802 https:\/\/doi.org\/10.1103\/PhysRevLett.108.120802 (2012).","journal-title":"Phys. Rev. Lett."},{"key":"11084_CR12","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1038\/s42254-021-00286-6","volume":"3","author":"K Beeks","year":"2021","unstructured":"Beeks, K. et al. The thorium-229 low-energy isomer and the nuclear clock. Nat. Rev. Phys. 3, 238\u2013248 https:\/\/doi.org\/10.1038\/s42254-021-00286-6 (2021).","journal-title":"Nat. Rev. Phys."},{"key":"11084_CR13","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1038\/s41586-024-07839-6","volume":"633","author":"C Zhang","year":"2024","unstructured":"Zhang, C. et al. Frequency ratio of the 229Th nuclear isomeric transition and the 87Sr atomic clock. Nature 633, 63\u201370 https:\/\/doi.org\/10.1038\/s41586-024-07839-6 (2024).","journal-title":"Nature"},{"key":"11084_CR14","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1038\/s41586-025-09999-5","volume":"650","author":"T Ooi","year":"2026","unstructured":"Ooi, T. et al. Frequency reproducibility of solid-state thorium-229 nuclear clocks. Nature 650, 72\u201378 https:\/\/doi.org\/10.1038\/s41586-025-09999-5 (2026).","journal-title":"Nature"},{"key":"11084_CR15","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-025-64191-7","volume":"16","author":"K Beeks","year":"2025","unstructured":"Beeks, K. et al. Fine-structure constant sensitivity of the Th-229 nuclear clock transition. Nat. Commun. 16, 9147 https:\/\/doi.org\/10.1038\/s41467-025-64191-7 (2025).","journal-title":"Nat. Commun."},{"key":"11084_CR16","doi-asserted-by":"publisher","unstructured":"Kawasaki, A. Quantum sensing using atomic clocks for nuclear and particle physics. Appl. Phys. Rev. 12, 041331 https:\/\/doi.org\/10.1063\/5.0273813 (2025).","DOI":"10.1063\/5.0273813"},{"key":"11084_CR17","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/0375-9474(76)90494-2","volume":"259","author":"L Kroger","year":"1976","unstructured":"Kroger, L. & Reich, C. Features of the low-energy level scheme of 229Th as observed in the \u03b1-decay of 233U. Nucl. Phys. A 259, 29\u201360 https:\/\/doi.org\/10.1016\/0375-9474(76)90494-2 (1976).","journal-title":"Nucl. Phys. A"},{"key":"11084_CR18","doi-asserted-by":"publisher","first-page":"R499","DOI":"10.1103\/PhysRevC.42.R499","volume":"42","author":"D Burke","year":"1990","unstructured":"Burke, D., Garrett, P., Qu, T. & Naumann, R. Additional evidence for the proposed excited state at \u22645\u2009eV in 229Th. Phys. Rev. C 42, R499 https:\/\/doi.org\/10.1103\/PhysRevC.42.R499 (1990).","journal-title":"Phys. Rev. C"},{"key":"11084_CR19","doi-asserted-by":"publisher","first-page":"1845","DOI":"10.1103\/PhysRevC.49.1845","volume":"49","author":"RG Helmer","year":"1994","unstructured":"Helmer, R. G. & Reich, C. W. An excited state of 229Th at 3.5 eV. Phys. Rev. C 49, 1845\u20131858 https:\/\/doi.org\/10.1103\/PhysRevC.49.1845 (1994).","journal-title":"Phys. Rev. C"},{"key":"11084_CR20","doi-asserted-by":"publisher","first-page":"142501","DOI":"10.1103\/PhysRevLett.98.142501","volume":"98","author":"BR Beck","year":"2007","unstructured":"Beck, B. R. et al. Energy splitting of the ground-state doublet in the nucleus 229Th. Phys. Rev. Lett. 98, 142501 https:\/\/doi.org\/10.1103\/PhysRevLett.98.142501 (2007).","journal-title":"Phys. Rev. Lett."},{"key":"11084_CR21","unstructured":"Beck, B. et al. Improved value for the energy splitting of the ground-state doublet in the nucleus 229mTh. In Proc. 12th International Conference on Nuclear Reaction Mechanisms LLNL-PROC-415170 (eds Cerutti, F. & Ferrari, A) https:\/\/www.osti.gov\/biblio\/964521 (OSTI, 2009)."},{"key":"11084_CR22","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1038\/nature17669","volume":"533","author":"L van der Wense","year":"2016","unstructured":"van der Wense, L. et al. Direct detection of the 229Th nuclear clock transition. Nature 533, 47\u201351\u00a0https:\/\/doi.org\/10.1038\/nature17669 (2016).","journal-title":"Nature"},{"key":"11084_CR23","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1038\/s41586-019-1533-4","volume":"573","author":"B Seiferle","year":"2019","unstructured":"Seiferle, B. et al. Energy of the 229Th nuclear clock transition. Nature 573, 243\u2013246 https:\/\/doi.org\/10.1038\/s41586-019-1533-4 (2019).","journal-title":"Nature"},{"key":"11084_CR24","doi-asserted-by":"publisher","first-page":"706","DOI":"10.1038\/s41586-023-05894-z","volume":"617","author":"S Kraemer","year":"2023","unstructured":"Kraemer, S. et al. Observation of the radiative decay of the 229Th nuclear clock isomer. Nature 617, 706\u2013710 https:\/\/doi.org\/10.1038\/s41586-023-05894-z (2023).","journal-title":"Nature"},{"key":"11084_CR25","doi-asserted-by":"publisher","first-page":"182501","DOI":"10.1103\/PhysRevLett.132.182501","volume":"132","author":"J Tiedau","year":"2024","unstructured":"Tiedau, J. et al. Laser excitation of the Th-229 nucleus. Phys. Rev. Lett. 132, 182501 https:\/\/doi.org\/10.1103\/PhysRevLett.132.182501 (2024).","journal-title":"Phys. Rev. Lett."},{"key":"11084_CR26","doi-asserted-by":"publisher","first-page":"013201","DOI":"10.1103\/PhysRevLett.133.013201","volume":"133","author":"R Elwell","year":"2024","unstructured":"Elwell, R. et al. Laser excitation of the 229Th nuclear isomeric transition in a solid-state host. Phys. Rev. Lett. 133, 013201 https:\/\/doi.org\/10.1103\/PhysRevLett.133.013201 (2024).","journal-title":"Phys. Rev. Lett."},{"key":"11084_CR27","doi-asserted-by":"publisher","first-page":"603","DOI":"10.1038\/s41586-024-08256-5","volume":"636","author":"C Zhang","year":"2024","unstructured":"Zhang, C. et al. 229ThF4 thin films for solid-state nuclear clocks. Nature 636, 603\u2013608 https:\/\/doi.org\/10.1038\/s41586-024-08256-5 (2024).","journal-title":"Nature"},{"key":"11084_CR28","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1038\/s41586-025-09776-4","volume":"648","author":"R Elwell","year":"2025","unstructured":"Elwell, R. et al. Laser-based conversion electron M\u00f6ssbauer spectroscopy of 229ThO2. Nature 648, 300\u2013305 https:\/\/doi.org\/10.1038\/s41586-025-09776-4 (2025).","journal-title":"Nature"},{"key":"11084_CR29","doi-asserted-by":"publisher","unstructured":"Hiraki, T. et al. Laser M\u00f6ssbauer spectroscopy of 229Th. Science 393, 795\u2013799 https:\/\/doi.org\/10.1126\/science.aea7978 (2026).","DOI":"10.1126\/science.aea7978"},{"key":"11084_CR30","doi-asserted-by":"publisher","first-page":"1971","DOI":"10.1364\/ASSL.2025.ATh3A.4","volume":"12","author":"V Lal","year":"2025","unstructured":"Lal, V. et al. Continuous-wave laser source at the 148\u2009nm nuclear transition of Th-229. Optica 12, 1971\u20131974 https:\/\/doi.org\/10.1364\/ASSL.2025.ATh3A.4 (2025).","journal-title":"Optica"},{"key":"11084_CR31","doi-asserted-by":"publisher","first-page":"852","DOI":"10.1038\/s41586-026-10107-4","volume":"650","author":"Q Xiao","year":"2026","unstructured":"Xiao, Q. et al. Continuous-wave narrow-linewidth vacuum ultraviolet laser source. Nature 650, 852\u2013856 https:\/\/doi.org\/10.1038\/s41586-026-10107-4 (2026).","journal-title":"Nature"},{"key":"11084_CR32","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-023-31045-5","volume":"13","author":"K Beeks","year":"2023","unstructured":"Beeks, K. et al. Growth and characterization of thorium-doped calcium fluoride single crystals. Sci. Rep. 13, 3897 https:\/\/doi.org\/10.1038\/s41598-023-31045-5 (2023).","journal-title":"Sci. Rep."},{"key":"11084_CR33","doi-asserted-by":"publisher","first-page":"094111","DOI":"10.1103\/PhysRevB.109.094111","volume":"109","author":"K Beeks","year":"2024","unstructured":"Beeks, K. et al. Optical transmission enhancement of ionic crystals via superionic fluoride transfer: growing VUV-transparent radioactive crystals. Phys. Rev. B 109, 094111 https:\/\/doi.org\/10.1103\/PhysRevB.109.094111 (2024).","journal-title":"Phys. Rev. B"},{"key":"11084_CR34","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1038\/416233a","volume":"416","author":"T Udem","year":"2002","unstructured":"Udem, T., Holzwarth, R. & H\u00e4nsch, T. W. Optical frequency metrology. Nature 416, 233\u2013237 https:\/\/doi.org\/10.1038\/416233a (2002).","journal-title":"Nature"},{"key":"11084_CR35","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1038\/s41586-019-1542-3","volume":"573","author":"T Masuda","year":"2019","unstructured":"Masuda, T. et al. X-ray pumping of the 229Th nuclear clock isomer. Nature 573, 238\u2013242 https:\/\/doi.org\/10.1038\/s41586-019-1542-3 (2019).","journal-title":"Nature"},{"key":"11084_CR36","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-024-49631-0","volume":"15","author":"T Hiraki","year":"2024","unstructured":"Hiraki, T. et al. Controlling 229Th isomeric state population in a VUV transparent crystal. Nat. Commun. 15, 5536 https:\/\/doi.org\/10.1038\/s41467-024-49631-0 (2024).","journal-title":"Nat. Commun."},{"key":"11084_CR37","doi-asserted-by":"publisher","first-page":"113801","DOI":"10.1103\/PhysRevLett.134.113801","volume":"134","author":"JS Higgins","year":"2025","unstructured":"Higgins, J. S. et al. Temperature sensitivity of a thorium-229 solid-state nuclear clock. Phys. Rev. Lett. 134, 113801 https:\/\/doi.org\/10.1103\/PhysRevLett.134.113801 (2025).","journal-title":"Phys. Rev. Lett."},{"key":"11084_CR38","doi-asserted-by":"publisher","first-page":"L022036","DOI":"10.1103\/PhysRevResearch.7.L022036","volume":"7","author":"F Schaden","year":"2025","unstructured":"Schaden, F. et al. Laser-induced quenching of the Th-229 nuclear clock isomer in calcium fluoride. Phys. Rev. Res. 7, L022036 https:\/\/doi.org\/10.1103\/PhysRevResearch.7.L022036 (2025).","journal-title":"Phys. Rev. Res."},{"key":"11084_CR39","doi-asserted-by":"publisher","first-page":"013203","DOI":"10.1103\/75bb-thn7","volume":"136","author":"M Guan","year":"2026","unstructured":"Guan, M. et al. X-ray-induced quenching of the 229Th clock isomer in CaF2. Phys. Rev. Lett. 136, 013203 https:\/\/doi.org\/10.1103\/75bb-thn7 (2026).","journal-title":"Phys. Rev. Lett."},{"key":"11084_CR40","doi-asserted-by":"crossref","unstructured":"Riley, W. Handbook of Frequency Stability Analysis https:\/\/tsapps.nist.gov\/publication\/get_pdf.cfm?pub_id=50505 (NIST, 2008).","DOI":"10.6028\/NIST.SP.1065"},{"key":"11084_CR41","doi-asserted-by":"crossref","unstructured":"Kimball, D. F. J. & van Bibber, K. (eds) The Search for Ultralight Bosonic Dark Matter (Springer International Publishing, 2023).","DOI":"10.1007\/978-3-030-95852-7_11"},{"key":"11084_CR42","doi-asserted-by":"publisher","first-page":"015015","DOI":"10.1103\/PhysRevD.91.015015","volume":"91","author":"A Arvanitaki","year":"2015","unstructured":"Arvanitaki, A., Huang, J. & Van Tilburg, K. Searching for dilaton dark matter with atomic clocks. Phys. Rev. D 91, 015015 https:\/\/doi.org\/10.1103\/PhysRevD.91.015015 (2015).","journal-title":"Phys. Rev. D"},{"key":"11084_CR43","doi-asserted-by":"publisher","first-page":"L031302","DOI":"10.1103\/l29n-gt5j","volume":"112","author":"A Caputo","year":"2025","unstructured":"Caputo, A. et al. Sensitivity of nuclear clocks to new physics. Phys. Rev. C 112, L031302 https:\/\/doi.org\/10.1103\/l29n-gt5j (2025).","journal-title":"Phys. Rev. C"},{"key":"11084_CR44","doi-asserted-by":"publisher","unstructured":"Arakawa, J. et al. Probing ultralight dark matter at the mega-Planck scale with the thorium nuclear clock. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2602.16804 (2026).","DOI":"10.48550\/arXiv.2602.16804"},{"key":"11084_CR45","doi-asserted-by":"publisher","first-page":"021055","DOI":"10.1103\/PhysRevX.15.021055","volume":"15","author":"E Fuchs","year":"2025","unstructured":"Fuchs, E. et al. Searching for dark matter with the 229Th nuclear lineshape from laser spectroscopy. Phys. Rev. X 15, 021055 https:\/\/doi.org\/10.1103\/PhysRevX.15.021055 (2025).","journal-title":"Phys. Rev. X"},{"key":"11084_CR46","unstructured":"Perlov, D. et al. Method for manufacturing of patterned SrB4BO7 and PbB4O7 crystals https:\/\/patents.justia.com\/patent\/11868022 US Patent 11,868,022 (2024)."},{"key":"11084_CR47","doi-asserted-by":"publisher","first-page":"1693","DOI":"10.1364\/OL.26.001693","volume":"26","author":"SC Buchter","year":"2001","unstructured":"Buchter, S. C. et al. Periodically poled BaMgF4 for ultraviolet frequency generation. Opt. Lett. 26, 1693\u20131695 https:\/\/doi.org\/10.1364\/OL.26.001693 (2001).","journal-title":"Opt. Lett."},{"key":"11084_CR48","doi-asserted-by":"publisher","unstructured":"Morgan, H. W. T. et al. A spinless crystal for a high-performance solid-state 229Th nuclear clock. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2503.11374 (2025).","DOI":"10.48550\/arXiv.2503.11374"},{"key":"11084_CR49","doi-asserted-by":"publisher","unstructured":"Aeppli, A. et al. (BACON Collaboration) Atomic clock frequency ratios with fractional uncertainty \u22643.2 \u00d7 10\u221218. Phys. Rev. Lett. 137, 033201 https:\/\/doi.org\/10.1103\/g865-9mk1 (2026).","DOI":"10.1103\/g865-9mk1"},{"key":"11084_CR50","unstructured":"Filzinger, M. et al. A multi-ion optical clock with 5\u00a0\u00d7\u00a010\u221219 uncertainty. Preprint at https:\/\/arxiv.org\/abs\/2603.23446 (2026)."},{"key":"11084_CR51","doi-asserted-by":"publisher","first-page":"033201","DOI":"10.1103\/hb3c-dk28","volume":"135","author":"MC Marshall","year":"2025","unstructured":"Marshall, M. C. et al. High-stability single-ion clock with 5.5\u00a0\u00d7\u00a010\u221219 systematic uncertainty. Phys. Rev. Lett. 135, 033201 https:\/\/doi.org\/10.1103\/hb3c-dk28 (2025).","journal-title":"Phys. Rev. Lett."},{"key":"11084_CR52","doi-asserted-by":"publisher","first-page":"253001","DOI":"10.1103\/PhysRevLett.130.253001","volume":"130","author":"M Filzinger","year":"2023","unstructured":"Filzinger, M. et al. Improved limits on the coupling of ultralight bosonic dark matter to photons from optical atomic clock comparisons. Phys. Rev. Lett. 130, 253001 https:\/\/doi.org\/10.1103\/PhysRevLett.130.253001 (2023).","journal-title":"Phys. Rev. Lett."},{"key":"11084_CR53","doi-asserted-by":"publisher","first-page":"564","DOI":"10.1038\/s41586-021-03253-4","volume":"591","author":"K Beloy","year":"2021","unstructured":"Boulder Atomic Clock Optical Network (BACON). Collaboration\u00a0Frequency ratio measurements at 18-digit accuracy using an optical clock network. Nature 591, 564\u2013569 https:\/\/doi.org\/10.1038\/s41586-021-03253-4 (2021).","journal-title":"Nature"},{"key":"11084_CR54","doi-asserted-by":"publisher","first-page":"061301","DOI":"10.1103\/PhysRevLett.117.061301","volume":"117","author":"A Hees","year":"2016","unstructured":"Hees, A., Gu\u00e9na, J., Abgrall, M., Bize, S. & Wolf, P. Searching for an oscillating massive scalar field as a dark matter candidate using atomic hyperfine frequency comparisons. Phys. Rev. Lett. 117, 061301 https:\/\/doi.org\/10.1103\/PhysRevLett.117.061301 (2016).","journal-title":"Phys. Rev. Lett."},{"key":"11084_CR55","doi-asserted-by":"publisher","first-page":"201302","DOI":"10.1103\/PhysRevLett.125.201302","volume":"125","author":"CJ Kennedy","year":"2020","unstructured":"Kennedy, C. J. et al. Precision metrology meets cosmology: improved constraints on ultralight dark matter from atom-cavity frequency comparisons. Phys. Rev. Lett. 125, 201302 https:\/\/doi.org\/10.1103\/PhysRevLett.125.201302 (2020).","journal-title":"Phys. Rev. Lett."},{"key":"11084_CR56","doi-asserted-by":"publisher","first-page":"241301","DOI":"10.1103\/PhysRevLett.129.241301","volume":"129","author":"T Kobayashi","year":"2022","unstructured":"Kobayashi, T. et al. Search for ultralight dark matter from long-term frequency comparisons of optical and microwave atomic clocks. Phys. Rev. Lett. 129, 241301 https:\/\/doi.org\/10.1103\/PhysRevLett.129.241301 (2022).","journal-title":"Phys. Rev. Lett."},{"key":"11084_CR57","doi-asserted-by":"publisher","first-page":"223001","DOI":"10.1103\/37vw-gc1r","volume":"135","author":"A Banerjee","year":"2025","unstructured":"Banerjee, A. et al. Oscillating nuclear charge radii as sensors for ultralight dark matter. Phys. Rev. Lett. 135, 223001 https:\/\/doi.org\/10.1103\/37vw-gc1r (2025).","journal-title":"Phys. Rev. Lett."},{"key":"11084_CR58","doi-asserted-by":"publisher","first-page":"121102","DOI":"10.1103\/PhysRevLett.129.121102","volume":"129","author":"P Touboul","year":"2022","unstructured":"Touboul, P. et al. MICROSCOPE mission: final results of the test of the equivalence principle. Phys. Rev. Lett. 129, 121102 https:\/\/doi.org\/10.1103\/PhysRevLett.129.121102 (2022).","journal-title":"Phys. Rev. Lett."},{"key":"11084_CR59","doi-asserted-by":"publisher","first-page":"022506","DOI":"10.1103\/PhysRevA.68.022506","volume":"68","author":"VA Dzuba","year":"2003","unstructured":"Dzuba, V. A., Flambaum, V. V. & Marchenko, M. V. Relativistic effects in Sr, Dy, Yb II, and Yb III and search for variation of the fine-structure constant. Phys. Rev. A 68, 022506 https:\/\/doi.org\/10.1103\/PhysRevA.68.022506 (2003).","journal-title":"Phys. Rev. A"},{"key":"11084_CR60","doi-asserted-by":"publisher","unstructured":"Beeks, K. The Nuclear Excitation of Thorium-229 in the CaF2 Environment: Development of a Crystalline Nuclear Clock. PhD thesis, TU Wien https:\/\/doi.org\/10.34726\/hss.2022.99008 (2022).","DOI":"10.34726\/hss.2022.99008"},{"key":"11084_CR61","doi-asserted-by":"publisher","first-page":"054703","DOI":"10.1063\/1.1898203","volume":"76","author":"E Rubiola","year":"2005","unstructured":"Rubiola, E. On the measurement of frequency and of its sample variance with high-resolution counters. Rev. Sci. Instrum. 76, 054703 https:\/\/doi.org\/10.1063\/1.1898203 (2005).","journal-title":"Rev. Sci. Instrum."},{"key":"11084_CR62","doi-asserted-by":"publisher","first-page":"918","DOI":"10.1109\/TUFFC.2007.337","volume":"54","author":"ST Dawkins","year":"2007","unstructured":"Dawkins, S. T., McFerran, J. J. & Luiten, A. N. Considerations on the measurement of the stability of oscillators with frequency counters. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 918\u2013925 (2007).","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"11084_CR63","doi-asserted-by":"publisher","unstructured":"Stuhler, J. et al. Industrial 171Yb+ single-ion optical clock with systematic uncertainty below 2\u00a0\u00d7\u00a010\u221217. In Proc. Quantum Sensing, Imaging, and Precision Metrology IV, Vol. 13920 (ed. Shahriar, S. M.) 1392009 https:\/\/doi.org\/10.1117\/12.3101264 (SPIE, 2026).","DOI":"10.1117\/12.3101264"},{"key":"11084_CR64","doi-asserted-by":"publisher","unstructured":"Karshenboim, S. G., Flambaum, V. & Peik, E. Atomic clocks and constraints on variations of fundamental constants. In Springer Handbook of Atomic, Molecular, and Optical Physics (ed. Drake, G. W. F.) 449\u2013459 https:\/\/doi.org\/10.1007\/978-3-030-73893-8_30 (Springer International Publishing, 2023).","DOI":"10.1007\/978-3-030-73893-8_30"},{"key":"11084_CR65","doi-asserted-by":"publisher","first-page":"835","DOI":"10.1086\/160554","volume":"263","author":"JD Scargle","year":"1982","unstructured":"Scargle, J. D. Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data. Astrophys. J. 263, 835\u2013853 https:\/\/doi.org\/10.1086\/160554 (1982).","journal-title":"Astrophys. J."},{"key":"11084_CR66","doi-asserted-by":"publisher","first-page":"084033","DOI":"10.1103\/PhysRevD.82.084033","volume":"82","author":"T Damour","year":"2010","unstructured":"Damour, T. & Donoghue, J. F. Equivalence principle violations and couplings of a light dilaton. Phys. Rev. D 82, 084033 https:\/\/doi.org\/10.1103\/PhysRevD.82.084033 (2010).","journal-title":"Phys. Rev. D"},{"key":"11084_CR67","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-021-27632-7","volume":"12","author":"GP Centers","year":"2021","unstructured":"Centers, G. P. et al. Stochastic fluctuations of bosonic dark matter. Nat. Commun. 12, 7321 https:\/\/doi.org\/10.1038\/s41467-021-27632-7 (2021).","journal-title":"Nat. Commun."},{"key":"11084_CR68","doi-asserted-by":"publisher","unstructured":"Astropy Collaboration, Price-Whelan, A. M. & Lim, P. L. et al. The Astropy project: sustaining and growing a community-oriented open-source project and the latest major release (v5.0) of the core package. Astrophys. J. https:\/\/doi.org\/10.3847\/1538-4357\/ac7c74 (2022).","DOI":"10.3847\/1538-4357\/ac7c74"},{"key":"11084_CR69","doi-asserted-by":"publisher","unstructured":"Lahs, S. A thorium-229 optical nuclear clock with feedback loop. Zenodo https:\/\/doi.org\/10.5281\/zenodo.22657608 (2026).","DOI":"10.5281\/zenodo.22657608"}],"container-title":["Nature"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41586-026-11084-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41586-026-11084-4","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41586-026-11084-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T08:13:19Z","timestamp":1791447199000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41586-026-11084-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,7]]},"references-count":69,"alternative-id":["11084"],"URL":"https:\/\/doi.org\/10.1038\/s41586-026-11084-4","relation":{},"ISSN":["0028-0836","1476-4687"],"issn-type":[{"value":"0028-0836","type":"print"},{"value":"1476-4687","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,7]]},"assertion":[{"value":"3 June 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 August 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 October 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","label":"Competing interests","group":{"name":"EthicsHeading","label":"Ethics"}}]}}