{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T10:57:32Z","timestamp":1790765852945,"version":"4.1.0"},"reference-count":67,"publisher":"Springer Science and Business Media LLC","issue":"8134","license":[{"start":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T00:00:00Z","timestamp":1790121600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T00:00:00Z","timestamp":1790121600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nature"],"published-print":{"date-parts":[[2026,10,1]]},"DOI":"10.1038\/s41586-026-11072-8","type":"journal-article","created":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T15:03:53Z","timestamp":1790175833000},"page":"60-64","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Lu+ optical frequency references with accuracy verified at the 19th digit"],"prefix":"10.1038","volume":"658","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3544-8246","authenticated-orcid":false,"given":"K. J.","family":"Arnold","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-6128-3097","authenticated-orcid":false,"given":"M. D. K.","family":"Lee","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-4401-2141","authenticated-orcid":false,"given":"Qi","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qichen","family":"Qin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1212-9173","authenticated-orcid":false,"given":"Zhao","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-7772-0030","authenticated-orcid":false,"given":"N.","family":"Jayjong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1483-8029","authenticated-orcid":false,"given":"M. D.","family":"Barrett","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,9,23]]},"reference":[{"key":"11072_CR1","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 (2015).","journal-title":"Rev. Mod. Phys."},{"key":"11072_CR2","doi-asserted-by":"publisher","first-page":"012001","DOI":"10.1088\/1681-7575\/ad17d2","volume":"61","author":"N Dimarcq","year":"2024","unstructured":"Dimarcq, N. et al. Roadmap towards the redefinition of the second. Metrologia 61, 012001 (2024).","journal-title":"Metrologia"},{"key":"11072_CR3","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1007\/s00190-016-0986-6","volume":"91","author":"G Lion","year":"2017","unstructured":"Lion, G. et al. Determination of a high spatial resolution geopotential model using atomic clock comparisons. J. Geod. 91, 597\u2013611 (2017).","journal-title":"J. Geod."},{"key":"11072_CR4","doi-asserted-by":"publisher","first-page":"064401","DOI":"10.1088\/1361-6633\/aab409","volume":"81","author":"TE Mehlst\u00e4ubler","year":"2018","unstructured":"Mehlst\u00e4ubler, T. E., Grosche, G., Lisdat, C., Schmidt, P. O. & Denker, H. Atomic clocks for geodesy. R. Prog. Phys. 81, 064401 (2018).","journal-title":"R. Prog. Phys."},{"key":"11072_CR5","doi-asserted-by":"publisher","first-page":"025008","DOI":"10.1103\/RevModPhys.90.025008","volume":"90","author":"M Safronova","year":"2018","unstructured":"Safronova, M. et al. Search for new physics with atoms and molecules. Rev. Mod. Phys. 90, 025008 (2018).","journal-title":"Rev. Mod. Phys."},{"key":"11072_CR6","doi-asserted-by":"publisher","first-page":"204","DOI":"10.1038\/s41586-019-0972-2","volume":"567","author":"C Sanner","year":"2019","unstructured":"Sanner, C. et al. Optical clock comparison for Lorentz symmetry testing. Nature 567, 204\u2013208 (2019).","journal-title":"Nature"},{"key":"11072_CR7","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1038\/s41566-020-0619-8","volume":"14","author":"M Takamoto","year":"2020","unstructured":"Takamoto, M. et al. Test of general relativity by a pair of transportable optical lattice clocks. Nat. Photon. 14, 411\u2013415 (2020).","journal-title":"Nat. Photon."},{"key":"11072_CR8","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 (2020).","journal-title":"Phys. Rev. Lett."},{"key":"11072_CR9","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 (2023).","journal-title":"Phys. Rev. Lett."},{"key":"11072_CR10","doi-asserted-by":"publisher","first-page":"210801","DOI":"10.1103\/PhysRevLett.113.210801","volume":"113","author":"RM Godun","year":"2014","unstructured":"Godun, R. M. et al. Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants. Phys. Rev. Lett. 113, 210801 (2014).","journal-title":"Phys. Rev. Lett."},{"key":"11072_CR11","doi-asserted-by":"publisher","first-page":"210802","DOI":"10.1103\/PhysRevLett.113.210802","volume":"113","author":"N Huntemann","year":"2014","unstructured":"Huntemann, N. et al. Improved limit on a temporal variation of mp\/me from comparisons of Yb+ and Cs atomic clocks. Phys. Rev. Lett. 113, 210802 (2014).","journal-title":"Phys. Rev. Lett."},{"key":"11072_CR12","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 (2025).","journal-title":"Phys. Rev. Lett."},{"key":"11072_CR13","doi-asserted-by":"publisher","first-page":"023401","DOI":"10.1103\/PhysRevLett.133.023401","volume":"133","author":"A Aeppli","year":"2024","unstructured":"Aeppli, A., Kim, K., Warfield, W., Safronova, M. S. & Ye, J. Clock with 8\u00a0\u00d7\u00a010\u221219 systematic uncertainty. Phys. Rev. Lett. 133, 023401 (2024).","journal-title":"Phys. Rev. Lett."},{"key":"11072_CR14","doi-asserted-by":"publisher","first-page":"053202","DOI":"10.1103\/vngc-c1xv","volume":"136","author":"B-I Zhang","year":"2026","unstructured":"Zhang, B.-I. et al. Liquid-nitrogen-cooled 40Ca+ ion optical clock with a systematic uncertainty of 4.4\u00a0\u00d7\u00a010\u221219. Phys. Rev. Lett. 136, 053202 (2026).","journal-title":"Phys. Rev. Lett."},{"key":"11072_CR15","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1038\/s41586-018-0738-2","volume":"564","author":"WF McGrew","year":"2018","unstructured":"McGrew, W. F. et al. Atomic clock performance enabling geodesy below the centimetre level. Nature 564, 87\u201390 (2018).","journal-title":"Nature"},{"key":"11072_CR16","doi-asserted-by":"publisher","first-page":"eadg1971","DOI":"10.1126\/sciadv.adg1971","volume":"9","author":"Z Zhiqiang","year":"2023","unstructured":"Zhiqiang, Z., Arnold, K. J., Kaewuam, R. & Barrett, M. D. 176Lu+ clock comparison at the 10\u221218 level via correlation spectroscopy. Sci. Adv. 9, eadg1971 (2023).","journal-title":"Sci. Adv."},{"key":"11072_CR17","doi-asserted-by":"publisher","first-page":"564","DOI":"10.1038\/s41586-021-03253-4","volume":"591","author":"Boulder Atomic Clock Optical Network (BACON) Collaboration.","year":"2021","unstructured":"Boulder Atomic Clock Optical Network (BACON) Collaboration. Frequency ratio measurements at 18-digit accuracy using an optical clock network. Nature 591, 564\u2013569 (2021).","journal-title":"Nature"},{"key":"11072_CR18","unstructured":"Boulder Atomic Clock Optical Network (BACON) Collaboration. Atomic clock frequency ratios with fractional uncertainty \u22643.2 \u00d7 10\u221218. Phys. Rev. Lett. 137, 033201 (2026)."},{"key":"11072_CR19","doi-asserted-by":"publisher","first-page":"015005","DOI":"10.1088\/1681-7575\/abc86f","volume":"58","author":"S D\u00f6rscher","year":"2021","unstructured":"D\u00f6rscher, S. et al. Optical frequency ratio of a 171Yb+ single-ion clock and a 87Sr lattice clock. Metrologia 58, 015005 (2021).","journal-title":"Metrologia"},{"key":"11072_CR20","unstructured":"Pizzocaro, M. et al. International optical clock comparison using the European optical fiber network. Phys. Rev. Res. 8, 033250 (2026)."},{"key":"11072_CR21","doi-asserted-by":"publisher","first-page":"012040","DOI":"10.1088\/1742-6596\/2889\/1\/012040","volume":"2889","author":"KJ Arnold","year":"2024","unstructured":"Arnold, K. J. et al. Validating a lutetium frequency reference. J. Phys. Conf. Ser. 2889, 012040 (2024).","journal-title":"J. Phys. Conf. Ser."},{"key":"11072_CR22","doi-asserted-by":"publisher","first-page":"033115","DOI":"10.1103\/PhysRevA.110.033115","volume":"110","author":"KJ Arnold","year":"2024","unstructured":"Arnold, K. J. et al. Enhanced micromotion compensation using a phase-modulated light field. Phys. Rev. A 110, 033115 (2024).","journal-title":"Phys. Rev. A"},{"key":"11072_CR23","doi-asserted-by":"publisher","first-page":"012805","DOI":"10.1103\/s23f-pnph","volume":"113","author":"MDK Lee","year":"2026","unstructured":"Lee, M. D. K. et al. Precision measurement of the 176Lu+ 3D1 microwave clock transitions. Phys. Rev. A 113, 012805 (2026).","journal-title":"Phys. Rev. A"},{"key":"11072_CR24","doi-asserted-by":"publisher","first-page":"013104","DOI":"10.1103\/hdl1-nwrn","volume":"114","author":"MD Barrett","year":"2026","unstructured":"Barrett, M. D. & Arnold, K. J. Analysis of collision-shift assessments in ion-based clocks. Phys. Rev. A 114, 013104 (2026).","journal-title":"Phys. Rev. A"},{"key":"11072_CR25","doi-asserted-by":"publisher","first-page":"103601","DOI":"10.1103\/3wtv-sty2","volume":"135","author":"K Kim","year":"2025","unstructured":"Kim, K. et al. Atomic coherence of 2 minutes and instability of 1.5\u00a0\u00d7\u00a010\u221218 at 1 s in a Wannier-Stark lattice clock. Phys. Rev. Lett. 135, 103601 (2025).","journal-title":"Phys. Rev. Lett."},{"key":"11072_CR26","doi-asserted-by":"publisher","first-page":"1215","DOI":"10.1126\/science.1240420","volume":"341","author":"N Hinkley","year":"2013","unstructured":"Hinkley, N. et al. An atomic clock with 10\u221218 instability. Science 341, 1215\u20131218 (2013).","journal-title":"Science"},{"key":"11072_CR27","doi-asserted-by":"publisher","first-page":"263402","DOI":"10.1103\/zbpb-6qxb","volume":"135","author":"X-Y Liu","year":"2025","unstructured":"Liu, X.-Y. et al. Zero-dead-time strontium lattice clock with a stability at 10\u221219 level. Phys. Rev. Lett. 135, 263402 (2025).","journal-title":"Phys. Rev. Lett."},{"key":"11072_CR28","doi-asserted-by":"publisher","first-page":"714","DOI":"10.1038\/s41566-019-0493-4","volume":"13","author":"E Oelker","year":"2019","unstructured":"Oelker, E. et al. Demonstration of 4.8\u00a0\u00d7\u00a010\u221217 stability at 1 s for two independent optical clocks. Nat. Photon. 13, 714\u2013719 (2019).","journal-title":"Nat. Photon."},{"key":"11072_CR29","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1007\/s00340-007-2867-4","volume":"89","author":"M Chwalla","year":"2007","unstructured":"Chwalla, M. et al. Precision spectroscopy with two correlated atoms. Appl. Phys. B 89, 483\u2013488 (2007).","journal-title":"Appl. Phys. B"},{"key":"11072_CR30","doi-asserted-by":"publisher","first-page":"160801","DOI":"10.1103\/PhysRevLett.106.160801","volume":"106","author":"C\u00a0W Chou","year":"2011","unstructured":"Chou, C. W., Hume, D. B., Thorpe, M. J., Wineland, D. J. & Rosenband, T. Quantum coherence between two atoms beyond Q\u00a0=\u00a01015. Phys. Rev. Lett. 106, 160801 (2011).","journal-title":"Phys. Rev. Lett."},{"key":"11072_CR31","doi-asserted-by":"publisher","first-page":"243602","DOI":"10.1103\/PhysRevLett.125.243602","volume":"125","author":"ER Clements","year":"2020","unstructured":"Clements, E. R. et al. Lifetime-limited interrogation of two independent 27Al+ clocks using correlation spectroscopy. Phys. Rev. Lett. 125, 243602 (2020).","journal-title":"Phys. Rev. Lett."},{"key":"11072_CR32","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1038\/s41567-022-01794-7","volume":"19","author":"ME Kim","year":"2023","unstructured":"Kim, M. E. et al. Improved interspecies optical clock comparisons through differential spectroscopy. Nat. Phys. 19, 25\u201329 (2023).","journal-title":"Nat. Phys."},{"key":"11072_CR33","doi-asserted-by":"publisher","first-page":"033801","DOI":"10.1103\/zgrm-cjbb","volume":"136","author":"D Lee","year":"2026","unstructured":"Lee, D. et al. Frequency stability of 2.5\u00a0\u00d7\u00a010\u221217 from a Si cavity with AlGaAs crystalline mirrors. Phys. Rev. Lett. 136, 033801 (2026).","journal-title":"Phys. Rev. Lett."},{"key":"11072_CR34","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1016\/S0030-4018(98)00121-7","volume":"150","author":"JE Bernard","year":"1998","unstructured":"Bernard, J. E., Marmet, L. M. & Madej, A. A. A laser frequency lock referenced to a single trapped ion. Opt. Commun. 150, 170\u2013174 (1998).","journal-title":"Opt. Commun."},{"key":"11072_CR35","doi-asserted-by":"publisher","first-page":"053024","DOI":"10.1088\/1367-2630\/17\/5\/053024","volume":"17","author":"MD Barrett","year":"2015","unstructured":"Barrett, M. D. Developing a field independent frequency reference. New J.Phys. 17, 053024 (2015).","journal-title":"New J.Phys."},{"key":"11072_CR36","doi-asserted-by":"publisher","first-page":"083202","DOI":"10.1103\/PhysRevLett.124.083202","volume":"124","author":"R Kaewuam","year":"2020","unstructured":"Kaewuam, R. et al. Hyperfine averaging by dynamic decoupling in a multi-ion lutetium clock. Phys. Rev. Lett. 124, 083202 (2020).","journal-title":"Phys. Rev. Lett."},{"key":"11072_CR37","doi-asserted-by":"publisher","first-page":"011804","DOI":"10.1103\/PhysRevA.82.011804","volume":"82","author":"VI Yudin","year":"2010","unstructured":"Yudin, V. I. et al. Hyper-Ramsey spectroscopy of optical clock transitions. Phys. Rev. A 82, 011804 (2010).","journal-title":"Phys. Rev. A"},{"key":"11072_CR38","doi-asserted-by":"publisher","first-page":"213002","DOI":"10.1103\/PhysRevLett.109.213002","volume":"109","author":"N Huntemann","year":"2012","unstructured":"Huntemann, N. et al. Generalized Ramsey excitation scheme with suppressed light shift. Phys. Rev. Lett. 109, 213002 (2012).","journal-title":"Phys. Rev. Lett."},{"key":"11072_CR39","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-018-04079-x","volume":"9","author":"KJ Arnold","year":"2018","unstructured":"Arnold, K. J., Kaewuam, R., Roy, A., Tan, T. R. & Barrett, M. D. Blackbody radiation shift assessment for a lutetium ion clock. Nat. Commun. 9, 1650 (2018).","journal-title":"Nat. Commun."},{"key":"11072_CR40","doi-asserted-by":"publisher","first-page":"012510","DOI":"10.1103\/PhysRevA.99.012510","volume":"99","author":"KJ Arnold","year":"2019","unstructured":"Arnold, K. J. et al. Dynamic polarizability measurements with 176Lu+. Phys. Rev. A 99, 012510 (2019).","journal-title":"Phys. Rev. A"},{"key":"11072_CR41","doi-asserted-by":"publisher","first-page":"193001","DOI":"10.1103\/PhysRevLett.124.193001","volume":"124","author":"KJ Arnold","year":"2020","unstructured":"Arnold, K. J. et al. Precision measurements of the 138Ba+ 6s2S1\/2 \u2013 5d2D5\/2 clock transition. Phys. Rev. Lett. 124, 193001 (2020).","journal-title":"Phys. Rev. Lett."},{"key":"11072_CR42","doi-asserted-by":"publisher","first-page":"052834","DOI":"10.1103\/PhysRevA.102.052834","volume":"102","author":"Z Zhiqiang","year":"2020","unstructured":"Zhiqiang, Z., Arnold, K. J., Kaewuam, R., Safronova, M. S. & Barrett, M. D. Hyperfine-mediated effects in a Lu+ optical clock. Phys. Rev. A 102, 052834 (2020).","journal-title":"Phys. Rev. A"},{"key":"11072_CR43","doi-asserted-by":"publisher","first-page":"033419","DOI":"10.1103\/PhysRevA.100.033419","volume":"100","author":"AM Hankin","year":"2019","unstructured":"Hankin, A. M. et al. Systematic uncertainty due to background-gas collisions in trapped-ion optical clocks. Phys. Rev. A 100, 033419 (2019).","journal-title":"Phys. Rev. A"},{"key":"11072_CR44","doi-asserted-by":"publisher","first-page":"022704","DOI":"10.1103\/PhysRevA.96.022704","volume":"96","author":"AC Vutha","year":"2017","unstructured":"Vutha, A. C., Kirchner, T. & Dub\u00e9, P. Collisional frequency shift of a trapped-ion optical clock. Phys. Rev. A 96, 022704 (2017).","journal-title":"Phys. Rev. A"},{"key":"11072_CR45","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 (2026).","journal-title":"Optica"},{"key":"11072_CR46","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1038\/s41567-017-0042-3","volume":"14","author":"J Grotti","year":"2018","unstructured":"Grotti, J. et al. Geodesy and metrology with a transportable optical clock. Nat. Phys. 14, 437\u2013441 (2018).","journal-title":"Nat. Phys."},{"key":"11072_CR47","doi-asserted-by":"publisher","first-page":"013005","DOI":"10.1088\/1367-2630\/ada4d1","volume":"27","author":"MD Barrett","year":"2025","unstructured":"Barrett, M. D. & Arnold, K. J. An extrapolation method for polarisability assessments of ion-based optical clocks. New J. Phys. 27, 013005 (2025).","journal-title":"New J. Phys."},{"key":"11072_CR48","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1007\/s00190-017-1075-1","volume":"92","author":"H Denker","year":"2018","unstructured":"Denker, H. et al. Geodetic methods to determine the relativistic redshift at the level of 10\u221218 in the context of international timescales: a review and practical results. J. Geod. 92, 487\u2013516 (2018).","journal-title":"J. Geod."},{"key":"11072_CR49","doi-asserted-by":"publisher","first-page":"033201","DOI":"10.1103\/PhysRevLett.123.033201","volume":"123","author":"SM Brewer","year":"2019","unstructured":"Brewer, S. M. et al. 27Al+ quantum-logic clock with a systematic uncertainty below 10\u221218. Phys. Rev. Lett. 123, 033201 (2019).","journal-title":"Phys. Rev. Lett."},{"key":"11072_CR50","doi-asserted-by":"publisher","first-page":"065004","DOI":"10.1088\/1681-7575\/ab4089","volume":"56","author":"T Bothwell","year":"2019","unstructured":"Bothwell, T. et al. JILA SrI optical lattice clock with uncertainty of 2.0\u00a0\u00d7\u00a010\u221218. Metrologia 56, 065004 (2019).","journal-title":"Metrologia"},{"key":"11072_CR51","doi-asserted-by":"publisher","first-page":"044082","DOI":"10.1103\/czlf-bfvp","volume":"24","author":"T Lindvall","year":"2025","unstructured":"Lindvall, T. et al. 88Sr+ optical clock with 7.9\u00a0\u00d7\u00a010\u221219 systematic uncertainty and measurement of its absolute frequency with 9.8\u00a0\u00d7\u00a010\u221217 uncertainty. Phys. Rev. Appl. 24, 044082 (2025).","journal-title":"Phys. Rev. Appl."},{"key":"11072_CR52","doi-asserted-by":"publisher","DOI":"10.1088\/1681-7575\/ae449e","volume":"63","author":"Z-P Jia","year":"2026","unstructured":"Jia, Z.-P. et al. Improved systematic evaluation of a strontium optical clock with uncertainty below 1\u00d710\u221218. Metrologia 63, 025002 (2026).","journal-title":"Metrologia"},{"key":"11072_CR53","doi-asserted-by":"publisher","first-page":"032808","DOI":"10.1103\/3gct-km6y","volume":"112","author":"Q Zhao","year":"2025","unstructured":"Zhao, Q. et al. Land\u00e9 g-factor measurements for the 5d6s 3D2 hyperfine levels of 176Lu+. Phys. Rev. A 112, 032808 (2025).","journal-title":"Phys. Rev. A"},{"key":"11072_CR54","doi-asserted-by":"publisher","first-page":"200502","DOI":"10.1103\/PhysRevLett.100.200502","volume":"100","author":"AH Myerson","year":"2008","unstructured":"Myerson, A. H. et al. High-fidelity readout of trapped-ion qubits. Phys. Rev. Lett. 100, 200502 (2008).","journal-title":"Phys. Rev. Lett."},{"key":"11072_CR55","doi-asserted-by":"publisher","first-page":"5025","DOI":"10.1063\/1.367318","volume":"83","author":"DJ Berkeland","year":"1998","unstructured":"Berkeland, D. J., Miller, J. D., Bergquist, J. C., Itano, W. M. & Wineland, D. J. Minimization of ion micromotion in a Paul trap. J. Appl. Phys. 83, 5025\u20135033 (1998).","journal-title":"J. Appl. Phys."},{"key":"11072_CR56","doi-asserted-by":"publisher","first-page":"063418","DOI":"10.1103\/PhysRevA.61.063418","volume":"61","author":"QA Turchette","year":"2000","unstructured":"Turchette, Q. A. et al. Heating of trapped ions from the quantum ground state. Phys. Rev. A 61, 063418 (2000).","journal-title":"Phys. Rev. A"},{"key":"11072_CR57","doi-asserted-by":"publisher","first-page":"013109","DOI":"10.1103\/tjwn-bq6b","volume":"113","author":"Q Qichen","year":"2026","unstructured":"Qichen, Q. et al. Zeeman degenerate sideband cooling in 176Lu+. Phys. Rev. A 113, 013109 (2026).","journal-title":"Phys. Rev. A"},{"key":"11072_CR58","doi-asserted-by":"publisher","first-page":"032803","DOI":"10.1103\/PhysRevA.106.032803","volume":"106","author":"VJ Mart\u00ednez-Lahuerta","year":"2022","unstructured":"Mart\u00ednez-Lahuerta, V. J., Eilers, S., Mehlst\u00e4ubler, T. E., Schmidt, P. O. & Hammerer, K. Ab initio quantum theory of mass defect and time dilation in trapped-ion optical clocks. Phys. Rev. A 106, 032803 (2022).","journal-title":"Phys. Rev. A"},{"key":"11072_CR59","doi-asserted-by":"publisher","first-page":"163602","DOI":"10.1103\/qhj9-pc2b","volume":"136","author":"G Sorci","year":"2026","unstructured":"Sorci, G., Foo, J., Leibfried, D., Sanner, C. & Pikovski, I. Quantum signatures of proper time in optical ion clocks. Phys. Rev. Lett. 136, 163602 (2026).","journal-title":"Phys. Rev. Lett."},{"key":"11072_CR60","doi-asserted-by":"publisher","first-page":"032514","DOI":"10.1103\/PhysRevA.98.032514","volume":"98","author":"HCJ Gan","year":"2018","unstructured":"Gan, H. C. J. et al. Oscillating-magnetic-field effects in high-precision metrology. Phys. Rev. A 98, 032514 (2018).","journal-title":"Phys. Rev. A"},{"key":"11072_CR61","doi-asserted-by":"publisher","first-page":"042819","DOI":"10.1103\/PhysRevA.102.042819","volume":"102","author":"R Kaewuam","year":"2020","unstructured":"Kaewuam, R. et al. Precision measurement of the 3D1 and 3D2 quadrupole moments in Lu+. Phys. Rev. A 102, 042819 (2020).","journal-title":"Phys. Rev. A"},{"key":"11072_CR62","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1070\/QEL17005","volume":"49","author":"SN Kuznetsov","year":"2019","unstructured":"Kuznetsov, S. N. et al. Effect of trapped-ion heating on generalised Ramsey methods for suppressing frequency shifts caused by a probe field in atomic clocks. Quantum Electron. 49, 429 (2019).","journal-title":"Quantum Electron."},{"key":"11072_CR63","doi-asserted-by":"publisher","first-page":"010501","DOI":"10.1103\/PhysRevA.93.010501","volume":"93","author":"R Hobson","year":"2016","unstructured":"Hobson, R. et al. Modified hyper-Ramsey methods for the elimination of probe shifts in optical clocks. Phys. Rev. A 93, 010501 (2016).","journal-title":"Phys. Rev. A"},{"key":"11072_CR64","doi-asserted-by":"publisher","first-page":"023408","DOI":"10.1103\/PhysRevA.96.023408","volume":"96","author":"T Zanon-Willette","year":"2017","unstructured":"Zanon-Willette, T., Lefevre, R., Taichenachev, A. V. & Yudin, V. I. Universal interrogation protocol with zero probe-field-induced frequency shift for quantum clocks and high-accuracy spectroscopy. Phys. Rev. A 96, 023408 (2017).","journal-title":"Phys. Rev. A"},{"key":"11072_CR65","doi-asserted-by":"publisher","first-page":"022515","DOI":"10.1103\/PhysRevA.99.022515","volume":"99","author":"KJ Arnold","year":"2019","unstructured":"Arnold, K. J., Kaewuam, R., Tan, T. R. & Barrett, M. D. Oscillating quadrupole effects in high-precision metrology. Phys. Rev. A 99, 022515 (2019).","journal-title":"Phys. Rev. A"},{"key":"11072_CR66","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/s00340-012-4952-6","volume":"107","author":"S Falke","year":"2012","unstructured":"Falke, S., Misera, M., Sterr, U. & Lisdat, C. Delivering pulsed and phase stable light to atoms of an optical clock. Appl. Phys. B 107, 301\u2013311 (2012).","journal-title":"Appl. Phys. B"},{"key":"11072_CR67","doi-asserted-by":"publisher","first-page":"035008","DOI":"10.1088\/1681-7575\/addc76","volume":"62","author":"Z Zhang","year":"2025","unstructured":"Zhang, Z. et al. Absolute frequency measurement of a Lu+ (3D1) optical frequency standard via link to international atomic time. Metrologia 62, 035008 (2025).","journal-title":"Metrologia"}],"container-title":["Nature"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41586-026-11072-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41586-026-11072-8","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41586-026-11072-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T10:02:00Z","timestamp":1790762520000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41586-026-11072-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,23]]},"references-count":67,"journal-issue":{"issue":"8134","published-print":{"date-parts":[[2026,10,1]]}},"alternative-id":["11072"],"URL":"https:\/\/doi.org\/10.1038\/s41586-026-11072-8","relation":{},"ISSN":["0028-0836","1476-4687"],"issn-type":[{"value":"0028-0836","type":"print"},{"value":"1476-4687","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,23]]},"assertion":[{"value":"8 December 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 August 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 September 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"}}]}}