Asian Journal of Physics Vol. 35, Nos 1 – 3 (2026) 123-139

Measuring space-time with optical lattice clocks

A M Guzmán1,2
1Universidad Nacional de Colombia, Departamento de Física, Bogotá. Colombia

2Universidad del Atlántico, Barranquilla, Colombia

In memory of Professor Gallieno Denardo, ICTP Italy


Time measurement has reached the accuracy required to observe the relativistic redshift that causes clocks to run slower in stronger gravitational fields, within terrestrial height differences of the order of centimeters. With this accuracy we are indeed measuring the four-dimensional spacetime continuum rather than performing separate measurements of distance and time. The best cesium microwave clocks measure the SI second to within one second in 100 million years, using the time-of-flight technique of a “cloud” of cold atoms. In 2001, Hidetoshi Katori of the University of Tokyo proposed the first clock of strontium atoms trapped in a horizontal optical lattice, with a transition at 430 THz in the red range of visible light. By the 2010s, this clock held the record for accuracy of one second in 15 billion years, exceeding the estimated age of the universe. In July 2024, Jun Ye’s group at JILA, NIST, presented a vertically oriented one-dimensional optical lattice clock of strontium atoms with a total systematic uncertainty of 8.1 × 10−19 in fractional frequency units, representing the lowest uncertainty of any clock to date. We provide a timeline of key scientific advancements, challenges, and progress in verifying the global consistency of optical clocks, a critical step toward the redefinition of the second by the International Committee on Weights and Measures, anticipated in 2030. Additionally, we highlight recent contributions of optical lattice clocks to quantum metrology, precision quantum sensing, fundamental physics invariance, and the exploration of the relationship between quantum physics and general relativity. © Anita Publications. All rights reserved.
Doi: xxx
Keywords: Optical lattice clocks, atomic clocks, Time standard


Peer Review Information
Method: Single- anonymous; Screened for Plagiarism? Yes
Buy this Article in Print © Anita Publications. All rights reserve

References

  1. Pound R V, Rebka G A, Gravitational Red-Shift in Nuclear Resonance, Phys Rev Lett, 3(1959)439; doi.org/10.1103/PhysRevLett.3.439.
  2. Pound R V, Rebka G A, Apparent Weight of Photons, Phys Rev Lett, 4(1960)337–341.
  3. Zheng X, Dolde J, Cambria M C, Lim H M, Kolkowitz S, A lab-based test of the gravitational redshift with a miniature clock network, Nat Commun, 14(2023)4886: doi.org/10.1038/s41467-023-40629-8.
  4. Aeppli A, Kim K, Warfield W, Safronova M S, Ye J, Clock with 8×10-19 Systematic Uncertainty, Phys Rev Lett, 133(2024); doi.org/10.1103/PhysRevLett.133.023401.
  5. Denker H, Denk T L, Voigt C,Weyers S, Peik E, Margolis H S, Delva P, Wolf P, Petit G, Geodetic methods to determine the relativistic redshift at the level of 10-18 in the context of international timescales: a review and practical results, J Geod, 92(2018)487–516.
  6. Phillips W D, Nobel Lecture: Laser cooling and trapping of neutral atoms, Rev Mod Phys, 70(1998)721; doi.org/10.1103/RevModPhys.70.721.
  7. Hänsch T W, Schawlow A L, Cooling of gases by laser radiation, Opt Commun, 13(1975)68–69.
  8. Wineland D J, Drullinger R E, Walls F L, Radiation-Pressure Cooling of Bound Resonant Absorbers, Phys Rev Lett, 40(1978)1639; doi.org/10.1103/PhysRevLett.40.1639
  9. Chu S, Hollberg L, Bjorkholm J E, Cable A, Ashkin A, Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure, Phys Rev Lett, 55(1985)48–51.
  10. Gould P L, Lett P D, Phillips W D, New measurements with optical molasses. In: Persson W and Svanberg S, (eds), Laser Spectroscopy VIII, (Springer, Berlin, Heidelberg), 1987, pp 64-67.
  11. Lett P D, Watts R N, Westbrook C I, Phillips W D, Gould P L, Metcalf H J, Observation of Atoms Laser Cooled below the Doppler Limit, Phys Rev Lett, 61(1988)169: doi.org/10.1103/PhysRevLett.61.169.
  12. Dalibard J, Cohen-Tannoudji C, Laser cooling below the Doppler limit by polarization gradients: simple theoretical models, J Opt Soc Am B, 6(1989)2023: doi.org/10.1364/JOSAB.6.002023.
  13. Westbrook C I, Watts R N, Tanner C E, Rolston S L, Phillips W D, Lett P D, Gould P L, Localization of atoms in a three-dimensional standing wave, Phys Rev Lett, 65(1990)33; doi.org/10.1103/PhysRevLett.65.33.
  14. Reichert J, Niering, Holzwarth M R, Weitz M, Udem Th, Hänsch T W, Phase Coherent Vacuum-Ultraviolet to Radio Frequency Comparison with a Mode-Locked Laser, Phys Rev Lett, 84(2000)3232; doi.org/10.1103/PhysRevLett.84.3232.
  15. Ludlow A D, Boyd M M, Ye J, Peik E, Schmidt P O, Optical atomic clocks, Rev Mod Phys, 87(2015)637: doi.org/10.1103/RevModPhys.87.637.
  16. Katori H, Takamoto M, Pal’chikov V G, Ovsiannikov V D, Ultrastable Optical Clock with Neutral Atoms in an Engineered Light Shift Trap, Phys Rev Lett, 91(2003)173005: doi.org//10.1103/PhysRevLett.91.173005.
  17. Ido T, Isoya Y, Katori H, Optical-dipole trapping of Sr atoms at a high phase-space density, Rev. A, 61(2000)061403; doi.org/10.1103/PhysRevA.61.061403.
  18. Wilpers G, Binnewies T, Degenhardt C, Sterr U, Helmcke J, Riehle F, Optical Clock with Ultracold Neutral Atoms, Phys Rev Lett, 89(2002)230801; doi.org/10.1103/PhysRevLett.89.230801.
  19. Guzmán A M, Meystre P, Dynamical effects of the dipole-dipole interaction in three-dimensional optical lattices, Phys Rev A, 57(1998)1139; doi.org/10.1103/PhysRevA.57.1139.
  20. Hassan Y S, K Beloy, JL Siegel, T Kobayashi, E Swiler, T Grogan, RC Brown, Rojo T, Bothwell T, Hunt B D, Halaoui A, Ludlow A D, Cryogenic Optical Lattice Clock with 1.7×10–20 Radiation Stark Uncertainty, Phys Rev Lett, 135(2025)063402; doi.org/10.1103/4tky-jmsm.
  21. Milner W R, Yan L, Hutson R B, Sanner C, Ye J, High-fidelity imaging of a band insulator in a three-dimensional optical lattice clock, Phys Rev A, 107(2023)063313; doi.org/10.1103/PhysRevA.107.063313.
  22. Zapata J, Guzmán A M, Moore M G, Meystre P, Gravity-induced Wannier-Stark ladder in an optical lattice, Phys Rev A, 63(2001)023607; doi.org/10.1103/PhysRevA.63.023607.
  23. Aeppli A, Chu A, Bothwell T, Kennedy C J, Kedar D, He P, Rey A M, Ye J, Hamiltonian engineering of spin-orbit–coupled fermions in a Wannier-Stark optical lattice clock, Sci Adv, 8(2022); doi.org/10.1126/sciadv.adc9242.
  24. Kim K, Aeppli A, Bothwell T, Ye J, Evaluation of Lattice Light Shift at Low 10-19 Uncertainty for a Shallow Lattice Sr Optical Clock, Phys Rev Lett, 130(2023)113203; doi.org/10.1103/PhysRevLett.130.113203.
  25. Boyd M M, Zelevinsky T, Ludlow A D, Blatt S, Zanon-Willette T, Foreman S M, Ye J, Nuclear spin effects in optical lattice clocks, Phys Rev A, 76(2007)022510; doi.org/10.1103/PhysRevA.76.022510.
  26. Yu H, Peng L, Yang L, Zhipeng J, Xiang Z, Jiarong Y, Ji L, Hanning D, Yuao C, Improved evaluation of blackbody radiation shift with uncertainty below 10–18 in a strontium lattice clock, Measurement, 257(2026)118527; doi.org/10.1016/j.measurement.2025.118527.
  27. Nicholson T L, Campbell S L, Hutson R B, Marti G E, Bloom B J, McNally R L, Zhang W, Barrett M D, Safronova M S, Strouse G F, Tew W L, Ye J, Systematic evaluation of an atomic clock at 2×10−18 total uncertainty, Nat Commun, 6(2015)6896: doi.org/10.1038/ncomms7896.
  28. Heo M-S, Kim H, Yu D-H, Lee W-K, Park C Y, Evaluation of the blackbody radiation shift of an Yb optical lattice clock at KRISS, Metrologia, 59(2022)055002: doi.org/10.1088/1681-7575/ac8483.
  29. Marshall M C, Castillo DAR, Arthur-Dworschack W J, Aeppli A, Kim K, Lee D, Warfield W, Hinrichs J, Nardelli N V, Fortier T M, Ye J, Leibrandt D R, Hum D B, High-Stability Single-Ion Clock with 5.5×10−19 Systematic Uncertainty, Phys Rev Lett, 135(2025)033201; doi.org/10.1103/hb3c-dk28
  30. Dimarcq N, Gertsvolf M, Mileti M G, Bize S, Oates C W, Peik E, Calonico D, Ido T, Tavella P, Meynadier F, Roadmap towards the redefinition of the second, Metrologia, 61(2024)012001; doi.org/10.1088/1681-7575/ad17d2.
  31. Kobayashi T, Nishiyama A, Hosaka K, Akamatsu D, Kawasaki A, Wada M, Inaba H, Tanabe T, Yasuda M, Improved absolute frequency measurement of 171Yb at NMIJ with uncertainty below 2×10−16, Metrologia, 62(2025)025006: doi.org/10.1088/1681-7575/adb754.
  32. McGrew W F, Zhang X, Fasano R F, Schäffer S A, Beloy K, Nicolodi D, Brown R C, Hinkley N, Milani G, Schioppo M, Yoon T H, Ludlow A D, Atomic clock performance enabling geodesy below the centimetre level, Nature, 564(2018)87: doi.org/10.1038/s41586-018-0738-2
  33. Nemitz N, Gotoh T, Nakagawa F, Ito H, Hanado Y, Ido T, Hachisu H, Absolute frequency of 87Sr at 1.8×10 −16 uncertainty by reference to remote primary frequency standards, Metrologia, 58(2021)025006; doi.org/10.1088/1681-7575/abc232.
  34. Goti I, Condio S, Clivati C, Risaro M, Gozzelino M, Costanzo G A, Levi F, Calonico D, and Pizzocaroet M, Absolute frequency measurement of a Yb optical clock at the limit of the Cs fountain, Metrologia, 60(2023)035002; doi.org/10.1088/1681-7575/accbc5.
  35. Oelker E, Hutson R B, Kennedy C J, Sonderhouse L, Bothwell T, Goban A, Kedar A D, Sanner C, Robinson J M, Marti G E, Matei D G, Legero T, Giunta M, Holzwarth R, Riehle F, Sterr U, Ye J, Demonstration of 4.8×10−17 stability at 1 s for two independent optical clocks, Nat Photonics, 13(2019)714: doi.org/10.1038/s41566-019-0493-4.
  36. Hausser H N, Hausser H N, Keller J, Nordmann T, Bhatt N M, Kiethe J, Liu H, Richter I M, von Boehn M, Rahm J, Weyers S, Benkler E, Lipphardt B, Dörscher S, Stahl K, Klose J, Lisdat C, Filzinger M, Huntemann N, Peik E, Mehlstäubler T E, 115In+–172Yb+ Coulomb crystal clock with 2.5×10−18 systematic uncertainty, Phys Rev Lett, 134(2025)023201; doi.org/10.1103/PhysRevLett.134.023201.
  37. Guzman A M, Moore M, Meystre P, Theory of a coherent atomic-beam generator, Phys Rev A, 53(1996)977: doi.org/10.1103/PhysRevA.53.97.
  38. Bilicki S, Bookjans E, Robyr J-L, Shi C, Vallet G, Le Targat R, Nicolodi D, Le Coq Y, Guéna J, Abgrall M, Rosenbusch P, Bize S, Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock, Metrologia, 53(2016)1123; doi.org/10.1088/0026-1394/53/4/1123.
  39. Margolis H S, Godun R M, Huntemann N, Targat R L, Pizzocaro M, Zawada M, Abgrall M, Akamatsu D , Martínez H Á, Amy-Klein A , Andia M , Benkler E , Bhatt N M, Bilicki S, Bize S, Bober M, Calonico D, Cambier V, Cantin E, Chardonnet C, Marín M C, Clivati C, Condio C-H, Curtis E A, Czubla A, Doležal M, Dörscher S, Dunst P, Feng C-H, Filzinger M, Folman R, Fordell T, Formichella V, Foucault Y, Galleani L, Goti I, Groswasser D, Gruszczyński M, Guo C, Hanhijärvi K J, Hausser H N, Hill I R, Hosaka K, Johnson MYH, Keller J, Klose J, Kobayashi T, Koke S, Kovačić D, Křen P, Kuhl A, Ledziński A, Lemański D, Levi F, Lindvall T, Lisdat C, Liu H, Lodewyck J, Lopez O, Lorini L, Lours M, Mašika P, M Mazouth-Laurol M, Mehlstaubler T E, Moreno W, Morzyński P, Narożnik M, Nawrocki J, Nishiyama A, Nogaś P, Nordmann T, Parsons A O, Pointard B, Pottie P E, Risaro M, Robertson B I, González J R, Schioppo M, Sesia I, Shang H, Signorile G, K Stahl K, Steinel M, Sterr U, Ramírez J S, Tofful A, Tønnes M, Tran A, Tunesi J, Wallin A E, Waterholter T , Zarei M, Zyskind C, Robust Optical Clocks for International Timescales (ROCIT), J Phys Conf Ser, 2889(2024)012022; doi.org/10.1088/1742-6596/2889/1/012022.
  40. Morzyński P, Bilicki S, Bober M, Kovacic D, Ciuryło R, Zawada M, Nawrocki J, Dunst P, Kobayashi T, Hosaka K, Akamatsu D, Intercontinental frequency ratio measurement of Yb and Sr optical lattice clocks, Metrologia, 61(2024)045009: doi.org/10.1088/1681-7575/ad6a1e.
  41. Katori H, Optical lattice clocks and quantum metrology, Nature Photon, 5(2011)203–210.
  42. Ye J, Zoller P, Essay, Quantum Sensing with Atomic, Molecular, and Optical Platforms for Fundamental Physics, Phys Rev Lett, 132(2024)190001; doi.org/10.1103/PhysRevLett.132.190001.
  43. Bothwell T, Kennedy C J, Aeppli A, Kedar D, Robinson J M, Oelker E, Staron A, JYe J, Resolving the gravitational redshift across a millimetre-scale atomic sample, Nature, 602(2022)420; doi.org/10.1038/s41586-021-04349-7.
  44. Chu A, Martínez-Lahuerta V J, Miklos M, Kim K, Zoller P, Hammerer K, Ye J, Rey A M, Exploring the Dynamical Interplay between Mass-Energy Equivalence, Interactions, and Entanglement in an Optical Lattice Clock, Phys Rev Lett, 134(2025)093201: doi.org/10.1103/PhysRevLett.134.093201.
  45. Derevianko A, Pospelov M, Hunting for topological dark matter with atomic clocks, Nat Phys, 10(2014)933–936.
  46. Boulder Atomic Clock Optical Network (BACON) Collaboration*. Frequency ratio measurements at 18-digit accuracy using an optical clock network, Nature, 591(2021)564–569: doi.org/10.1038/s41586-021-03253-4
  47. Kolkowitz S, Pikovski I, Langellier N, Lukin M D, Walsworth R L, J. Ye J, Gravitational wave detection with optical lattice atomic clocks, Phys Rev D, 94(2016)124043; doi.org/10.1103/PhysRevD.94.124043.
  48. Tino G M, Bassi A, Bianco G, Bongs K, Bouyer P, Cacciapuoti L, Capozziello S, Chen X, Chiofalo M L, Derevianko A, Ertmer W, Gaaloul N, Gill P, Graham P W, Hogan J M, Iess L, Kasevich M A, Katori H, Klempt C, Lu X, Ma L-S, Muller H, Newbury N R, Oates C W, Peters A, Poli N, Rasel E M, Rosi G, Roura A, Salomon C, Schiller S, Schleich W, Schlippert D, Schreck F, Schubert C, Sorrentino F, Sterr U, Thomsen J W, Vallone G, Vetrano F, Villoresi P, von Klitzing W, Wilkowski D, Wolf P, Ye J, Yu N, Zhan M, SAGE: A proposal for a space atomic gravity explorer, Eur Phys J: D 73(2019)228; doi.org/10.1140/epjd/e2019-100324-6.
  49. Blatt S, Ludlow A D, Campbell G K, Thomsen J W, ZelevinskyT, Boyd M M, Ye J, Baillard X, M. Fouche M, Targat R L, Brusch, Lemonde P, Takamoto M, Hong F.-L, Katori H, Flambaum V V, New Limits on Coupling of Fundamental Constants to Gravity Using 87Sr Optical Lattice Clocks, Phys Rev Lett, 100(2008)140801; doi.org/10.1103/PhysRevLett.100.140801.
  50. Lorini L, Ashby N, Brusch A, Diddams S, Drullinger R, Eason E, Fortier T, Hastings P, Heavner T, Hume D, Itano W, Jefferts S, Newbury N, Parker T, Rosenband W T, Stalnaker J, Swann W, Wineland D, Bergquist J, Recent atomic clock comparisons at NIST, Eur Phys J Spec Top, 163(2008)19; doi.org/10.1140/epjst/e2008-00807-7.
  51. Bauch A, Weyers S, New experimental limit on the validity of local position invariance, Phys Rev D, 65(2002)081101; doi.org/10.1103/PhysRevD.65.081101.
  52. Caldwell E D, Deschenes J D, Ellis J, Swann W C, Stuhl B K, Bergeron H, Newbury N R, Sinclair L C, Quantum-limited optical time transfer for future geosynchronous links, Nature, 618(2023)721–726.
  53. Kómár P, Kessler E, Bishof M, Jiang L, Sørensen A S, Ye J, Lukin M D, A quantum network of clocks, Nature Phys, 10(2014)582–587.
  54. Shinkai H, Takamoto M, Katori H, Transportable optical lattice clocks and general relativity, Int J Mod Phys: D, 34(2025)2540012; doi.org/10.1142/S0218271825400127.
  55. Takano T, Takamoto M, Ushijima I, Ohmae N, Akatsuka T, Yamaguchi A, Kuroishi Y, Munekane H, Miyahara B, Katori H, Geopotential measurements with synchronously linked optical lattice clocks, Nat Photon, 10(2016)662; doi.org/10.1038/nphoton.2016.159.
  56. Takamoto M, Ushijima I, Ohmae N, Yahagi T, Kokado K, Shinkai  H, Katori  H, Test of general relativity by a pair of transportable optical lattice clocks, Nat Photon, 14(2020)411–415.
  57. International Clock and Oscillator Networking (ICON) Collaboration, Amy-Klein A, et al., International comparison of optical frequencies with transportable optical lattice clocks, arXiv:2410.22973 (2024): 10.48550/arXiv.2410.22973