Questioning basic assumptions about the structure of space and time has greatly enhanced our understanding of nature. State-of-the-art atomic clocks1,2,3 make it possible to precisely test fundamental symmetry properties of spacetime and search for physics beyond the standard model at low energies of just a few electronvolts4. Modern tests of Einstein’s theory of relativity try to measure so-far-undetected violations of Lorentz symmetry5; accurately comparing the frequencies of optical clocks is a promising route to further improving such tests6. Here we experimentally demonstrate agreement between two single-ion optical clocks at the 10−18 level, directly validating their uncertainty budgets, over a six-month comparison period. The ytterbium ions of the two clocks are confined in separate ion traps with quantization axes aligned along non-parallel directions. Hypothetical Lorentz symmetry violations5,6,7 would lead to periodic modulations of the frequency offset as the Earth rotates and orbits the Sun. From the absence of such modulations at the 10−19 level we deduce stringent limits of the order of 10−21 on Lorentz symmetry violation parameters for electrons, improving previous limits8,9,10 by two orders of magnitude. Such levels of precision will be essential for low-energy tests of future quantum gravity theories describing dynamics at the Planck scale4, which are expected to predict the magnitude of residual symmetry violations.
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All data obtained in the study are available from the corresponding author on reasonable request.
Nicholson, T. L. et al. Systematic evaluation of an atomic clock at 2 × 10−18 total uncertainty. Nat. Commun. 6, 6896 (2015).
Huntemann, N., Sanner, C., Lipphardt, B., Tamm, C. & Peik, E. Single-ion atomic clock with 3 × 10−18 systematic uncertainty. Phys. Rev. Lett. 116, 063001 (2016).
McGrew, W. F. et al. Atomic clock performance enabling geodesy below the centimetre level. Nature 564, 87–90 (2018).
Safronova, M. S. et al. Search for new physics with atoms and molecules. Rev. Mod. Phys. 90, 025008 (2018).
Mattingly, D. Modern tests of Lorentz invariance. Living Rev. Relativ. 8, lrr-2005-5 (2005).
Kostelecký, V. A. & Vargas, A. J. Lorentz and CPT tests with clock-comparison experiments. Phys. Rev. D 98, 036003 (2018).
Colladay, D. & Kostelecký, V. A. Lorentz-violating extension of the standard model. Phys. Rev. D 58, 116002 (1998).
Altschul, B. Synchrotron and inverse Compton constraints on Lorentz violations for electrons. Phys. Rev. D 74, 083003 (2006).
Hohensee, M. A. et al. Limits on violations of Lorentz symmetry and the Einstein equivalence principle using radio-frequency spectroscopy of atomic dysprosium. Phys. Rev. Lett. 111, 050401 (2013).
Pruttivarasin, T. et al. Michelson–Morley analogue for electrons using trapped ions to test Lorentz symmetry. Nature 517, 592–595 (2015).
Kennedy, R. J. & Thorndike, E. M. Experimental establishment of the relativity of time. Phys. Rev. 42, 400–418 (1932).
Kostelecký, V. A. & Russell, N. Data tables for Lorentz and CPT violation. Rev. Mod. Phys. 83, 11–31 (2011).
Hughes, V. W., Robinson, H. G. & Beltran-Lopez, V. Upper limit for the anisotropy of inertial mass from nuclear resonance experiments. Phys. Rev. Lett. 4, 342–344 (1960).
Drever, R. W. P. A search for anisotropy of inertial mass using a free precession technique. Philos. Mag. 6, 683–687 (1961).
Müller, H., Herrmann, S., Saenz, A., Peters, A. & Lämmerzahl, C. Optical cavity tests of Lorentz invariance for the electron. Phys. Rev. D 68, 116006 (2003).
Müller, H. Testing Lorentz invariance by the use of vacuum and matter filled cavity resonators. Phys. Rev. D 71, 045004 (2005).
Megidish, E., Broz, J., Greene, N. & Häffner, H. Entanglement enhanced precision test of local Lorentz invariance. Preprint at https://arxiv.org/abs/1809.09807 (2018).
Campbell, S. L. et al. A Fermi-degenerate three-dimensional optical lattice clock. Science 358, 90–94 (2017).
Dzuba, V. A. et al. Strongly enhanced effects of Lorentz symmetry violation in entangled Yb+ ions. Nat. Phys. 12, 465–468 (2016).
Kostelecký, V. A. & Lane, C. D. Constraints on Lorentz violation from clock-comparison experiments. Phys. Rev. D 60, 116010 (1999).
Kostelecký, V. A. & Mewes, M. Signals for Lorentz violation in electrodynamics. Phys. Rev. D 66, 056005 (2002).
Kostelecký, V. A. & Tasson, J. D. Matter-gravity couplings and Lorentz violation. Phys. Rev. D 83, 016013 (2011).
Ludlow, A. D., Boyd, M. M., Ye, J., Peik, E. & Schmidt, P. O. Optical atomic clocks. Rev. Mod. Phys. 87, 637–701 (2015).
Tamm, C. et al. Cs-based optical frequency measurement using cross-linked optical and microwave oscillators. Phys. Rev. A 89, 023820 (2014).
Roos, C. F., Chwalla, M., Kim, K., Riebe, M. & Blatt, R. ‘Designer atoms’ for quantum metrology. Nature 443, 316–319 (2006).
Bluhm, R., Kostelecký, V. A., Lane, C. D. & Russell, N. Probing Lorentz and CPT violation with space-based experiments. Phys. Rev. D 68, 125008 (2003).
Matei, D. G. et al. 1.5 μm lasers with sub-10 mHz linewidth. Phys. Rev. Lett. 118, 263202 (2017).
Zanon-Willette, T. et al. Composite laser-pulses spectroscopy for high-accuracy optical clocks: a review of recent progress and perspectives. Rep. Prog. Phys. 81, 094401 (2018).
Yudin, V. I. et al. Hyper-Ramsey spectroscopy of optical clock transitions. Phys. Rev. A 82, 011804 (2010).
Taichenachev, A. V. et al. Compensation of field-induced frequency shifts in Ramsey spectroscopy of optical clock transitions. JETP Lett. 90, 713–717 (2010).
Delva, P. et al. Test of special relativity using a fiber network of optical clocks. Phys. Rev. Lett. 118, 221102 (2017).
Shaniv, R. et al. New methods for testing Lorentz invariance with atomic systems. Phys. Rev. Lett. 120, 103202 (2018).
Doležal, M. et al. Analysis of thermal radiation in ion traps for optical frequency standards. Metrologia 52, 842–856 (2015).
Keller, J., Partner, H. L., Burgermeister, T. & Mehlstäubler, T. E. Precise determination of micromotion for trapped-ion optical clocks. J. Appl. Phys. 118, 104501 (2015); correction 119, 059902 (2016).
Dubé, P., Madej, A. A., Zhou, Z. & Bernard, J. E. Evaluation of systematic shifts of the 88Sr+ single-ion optical frequency standard at the 10−17 level. Phys. Rev. A 87, 023806 (2013).
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).
Rosenband, T. et al. Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place. Science 319, 1808–1812 (2008).
We thank B. Altschul, A. Goban, R. Hutson, A. Kostelecký, T. Mehlstäubler, M. Mewes, A. Vargas-Silva and J. Zhang for discussions and B. Lipphardt for experimental assistance. This research received funding from the European Metrology Programme for Innovation and Research (EMPIR project OC18), co-financed by the Participating States and the European Union’s Horizon 2020 research and innovation programme, and from DFG through CRC 1227 (DQ-mat). This work was also supported in part by the Office of Naval Research, USA, under award number N00014-17-1-2252, by NSF through grant PHY-1620687 (USA) and by the Russian Foundation for Basic Research under grant number 17-02-00216. C.S. thanks the Humboldt Foundation for support.
The authors declare no competing interests.
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Sanner, C., Huntemann, N., Lange, R. et al. Optical clock comparison for Lorentz symmetry testing. Nature 567, 204–208 (2019). https://doi.org/10.1038/s41586-019-0972-2
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