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An elementary quantum network of entangled optical atomic clocks


Optical atomic clocks are our most precise tools to measure time and frequency1,2,3. Precision frequency comparisons between clocks in separate locations enable one to probe the space–time variation of fundamental constants4,5 and the properties of dark matter6,7, to perform geodesy8,9,10 and to evaluate systematic clock shifts. Measurements on independent systems are limited by the standard quantum limit; measurements on entangled systems can surpass the standard quantum limit to reach the ultimate precision allowed by quantum theory—the Heisenberg limit. Although local entangling operations have demonstrated this enhancement at microscopic distances11,12,13,14,15,16, comparisons between remote atomic clocks require the rapid generation of high-fidelity entanglement between systems that have no intrinsic interactions. Here we report the use of a photonic link17,18 to entangle two 88Sr+ ions separated by a macroscopic distance19 (approximately 2 m) to demonstrate an elementary quantum network of entangled optical clocks. For frequency comparisons between the ions, we find that entanglement reduces the measurement uncertainty by nearly \(\sqrt{2}\), the value predicted for the Heisenberg limit. Today’s optical clocks are typically limited by dephasing of the probe laser20; in this regime, we find that entanglement yields a factor of 2 reduction in the measurement uncertainty compared with conventional correlation spectroscopy techniques20,21,22. We demonstrate this enhancement for the measurement of a frequency shift applied to one of the clocks. This two-node network could be extended to additional nodes23, to other species of trapped particles or—through local operations—to larger entangled systems.

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Fig. 1: Network of entangled optical clocks.
Fig. 2: Spectroscopy with and without entanglement.
Fig. 3: Characterization of entanglement enhancement.
Fig. 4: Measurement of clock–clock frequency difference with and without entanglement.

Data availability

Source data for all plots are available. All other data or analysis code that support the plots are available from the corresponding authors upon reasonable request.


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

    ADS  CAS  PubMed  Article  Google Scholar 

  2. Oelker, E. et al. Demonstration of 4.8 × 10−17 stability at 1 s for two independent optical clocks. Nat. Photonics 13, 714–719 (2019).

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  4. 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).

    ADS  CAS  PubMed  Article  Google Scholar 

  5. Lange, R. et al. Improved limits for violations of local position invariance from atomic clock comparisons. Phys. Rev. Lett. 126, 011102 (2021).

    ADS  CAS  PubMed  Article  Google Scholar 

  6. Derevianko, A. & Pospelov, M. Hunting for topological dark matter with atomic clocks. Nat. Phys. 10, 933–936 (2014).

    CAS  Article  Google Scholar 

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

    ADS  MathSciNet  CAS  Article  Google Scholar 

  8. Chou, C.-W., Hume, D. B., Rosenband, T. & Wineland, D. J. Optical clocks and relativity. Science 329, 1630–1633 (2010).

    ADS  CAS  PubMed  Article  Google Scholar 

  9. Mehlstäubler, T. E., Grosche, G., Lisdat, C., Schmidt, P. O. & Denker, H. Atomic clocks for geodesy. Rep. Prog. Phys. 81, 064401 (2018).

    ADS  PubMed  Article  CAS  Google Scholar 

  10. McGrew, W. et al. Atomic clock performance enabling geodesy below the centimetre level. Nature 564, 87–90 (2018).

    ADS  CAS  PubMed  Article  Google Scholar 

  11. Meyer, V. et al. Experimental demonstration of entanglement-enhanced rotation angle estimation using trapped ions. Phys. Rev. Lett. 86, 5870–5873 (2001).

    ADS  CAS  PubMed  Article  Google Scholar 

  12. Leibfried, D. et al. Toward Heisenberg-limited spectroscopy with multiparticle entangled states. Science 304, 1476–1478 (2004).

    ADS  CAS  PubMed  Article  Google Scholar 

  13. Roos, C. F., Chwalla, M., Kim, K., Riebe, M. & Blatt, R. ‘Designer atoms’ for quantum metrology. Nature 443, 316–319 (2006).

    ADS  CAS  PubMed  Article  Google Scholar 

  14. Megidish, E., Broz, J., Greene, N. & Häffner, H. Improved test of local Lorentz invariance from a deterministic preparation of entangled states. Phys. Rev. Lett. 122, 123605 (2019).

    ADS  CAS  PubMed  Article  Google Scholar 

  15. Manovitz, T., Shaniv, R., Shapira, Y., Ozeri, R. & Akerman, N. Precision measurement of atomic isotope shifts using a two-isotope entangled state. Phys. Rev. Lett. 123, 203001 (2019).

    ADS  CAS  PubMed  Article  Google Scholar 

  16. Pedrozo-Peñafiel, E. et al. Entanglement on an optical atomic-clock transition. Nature 588, 414–418 (2020).

    ADS  PubMed  Article  CAS  Google Scholar 

  17. Moehring, D. L. et al. Entanglement of single-atom quantum bits at a distance. Nature 449, 68–71 (2007).

    ADS  CAS  PubMed  Article  Google Scholar 

  18. Monroe, C. et al. Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects. Phys. Rev. A 89, 022317 (2014).

    ADS  Article  CAS  Google Scholar 

  19. Stephenson, L. J. et al. High-rate, high-fidelity entanglement of qubits across an elementary quantum network. Phys. Rev. Lett. 124, 110501 (2020).

    ADS  CAS  PubMed  Article  Google Scholar 

  20. Clements, E. R. et al. Lifetime-limited interrogation of two independent 27Al+ clocks using correlation spectroscopy. Phys. Rev. Lett. 125, 243602 (2020).

    ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

  21. Hume, D. B. & Leibrandt, D. R. Probing beyond the laser coherence time in optical clock comparisons. Phys. Rev. A 93, 032138 (2016).

    ADS  Article  Google Scholar 

  22. Kim, M. E. et al. Optical coherence between atomic species at the second scale: improved clock comparisons via differential spectroscopy. Preprint at (2021).

  23. Komar, P. et al. A quantum network of clocks. Nat. Phys. 10, 582–587 (2014).

    CAS  Article  Google Scholar 

  24. Wineland, D. J., Bollinger, J. J., Itano, W. M., Moore, F. & Heinzen, D. J. Spin squeezing and reduced quantum noise in spectroscopy. Phys. Rev. A 46, R6797 (1992).

    ADS  CAS  PubMed  Article  Google Scholar 

  25. Wineland, D. J., Bollinger, J. J., Itano, W. M. & Heinzen, D. Squeezed atomic states and projection noise in spectroscopy. Phys. Rev. A 50, 67 (1994).

    ADS  CAS  PubMed  Article  Google Scholar 

  26. Degen, C. L., Reinhard, F. & Cappellaro, P. Quantum sensing. Rev. Mod. Phys. 89, 035002 (2017).

    ADS  MathSciNet  Article  Google Scholar 

  27. Pezzè, L., Smerzi, A., Oberthaler, M. K., Schmied, R. & Treutlein, P. Quantum metrology with nonclassical states of atomic ensembles. Rev. Mod. Phys. 90, 035005 (2018).

    ADS  MathSciNet  Article  Google Scholar 

  28. Caves, C. M. Quantum-mechanical noise in an interferometer. Phys. Rev. D 23, 1693 (1981).

    ADS  Article  Google Scholar 

  29. Tse, M. et al. Quantum-enhanced advanced LIGO detectors in the era of gravitational-wave astronomy. Phys. Rev. Lett. 123, 231107 (2019).

    ADS  CAS  PubMed  Article  Google Scholar 

  30. Malnou, M. et al. Squeezed vacuum used to accelerate the search for a weak classical signal. Phys. Rev. X 9, 021023 (2019).

    CAS  Google Scholar 

  31. Wolf, F. et al. Motional Fock states for quantum-enhanced amplitude and phase measurements with trapped ions. Nat. Commun. 10, 2929(2019).

    ADS  PubMed  PubMed Central  Article  CAS  Google Scholar 

  32. Gilmore, K. A. et al. Quantum-enhanced sensing of displacements and electric fields with two-dimensional trapped-ion crystals. Science 373, 673–678 (2021).

    ADS  CAS  PubMed  Article  Google Scholar 

  33. Kimble, H. J. The quantum internet. Nature 453, 1023–1030 (2008).

    ADS  CAS  PubMed  Article  Google Scholar 

  34. Gisin, N., Ribordy, G., Tittel, W. & Zbinden, H. Quantum cryptography. Rev. Mod. Phys. 74, 145–195 (2002).

    ADS  MATH  Article  Google Scholar 

  35. Monroe, C. & Kim, J. Scaling the ion trap quantum processor. Science 339, 1164–1169 (2013).

    ADS  CAS  PubMed  Article  Google Scholar 

  36. Hensen, B. et al. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature 526, 682–686 (2015).

    ADS  CAS  PubMed  Article  Google Scholar 

  37. Ramsey, N. F. A molecular beam resonance method with separated oscillating fields. Phys. Rev. 78, 695–699 (1950).

    ADS  CAS  Article  Google Scholar 

  38. Ramsey, N. F. Resonance experiments in successive oscillatory fields. Rev. Sci. Instrum. 28, 57–58 (1957).

    ADS  Article  Google Scholar 

  39. Itano, W. M. et al. Quantum projection noise: population fluctuations in two-level systems. Phys. Rev. A 47, 3554 (1993).

    ADS  CAS  PubMed  Article  Google Scholar 

  40. Giovannetti, V., Lloyd, S. & Maccone, L. Quantum metrology. Phys. Rev. Lett. 96, 010401 (2006).

    ADS  MathSciNet  PubMed  Article  CAS  Google Scholar 

  41. Riis, E. & Sinclair, A. G. Optimum measurement strategies for trapped ion optical frequency standards. J. Phys. B 37, 4719–4732 (2004).

    ADS  CAS  Article  Google Scholar 

  42. Leroux, I. D. et al. On-line estimation of local oscillator noise and optimisation of servo parameters in atomic clocks. Metrologia 54, 307–321 (2017).

    ADS  CAS  Article  Google Scholar 

  43. Bize, S. et al. Interrogation oscillator noise rejection in the comparison of atomic fountains. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1253–1255 (2000).

    CAS  PubMed  Article  Google Scholar 

  44. Chwalla, M. et al. Precision spectroscopy with two correlated atoms. Appl. Phys. B 89, 483–488 (2007).

    ADS  CAS  Article  Google Scholar 

  45. Marti, G. E. et al. Imaging optical frequencies with 100 μHz precision and 1.1 μm resolution. Phys. Rev. Lett. 120, 103201 (2018).

    ADS  CAS  PubMed  Article  Google Scholar 

  46. Young, A. W. et al. Half-minute-scale atomic coherence and high relative stability in a tweezer clock. Nature 588, 408–413 (2020).

    ADS  CAS  PubMed  Article  Google Scholar 

  47. Nadlinger, D. P. et al. Experimental quantum key distribution certified by Bell's theorem. Nature 607, 682–686 (2022).

  48. Stephenson, L. Entanglement between Nodes of a Quantum Network. Ph.D. thesis, Univ. of Oxford (2019).

  49. Sahoo, B. K., Islam, M. R., Das, B. P., Chaudhuri, R. K. & Mukherjee, D. Lifetimes of the metastable 2D3/2,5/2 states in Ca+, Sr+, and Ba+. Phys. Rev. A 74, 062504 (2006).

    ADS  Article  CAS  Google Scholar 

  50. Gabrielse, G. & Tan, J. Self-shielding superconducting solenoid systems. J. Appl. Phys 63, 5143–5148 (1988).

    ADS  Article  Google Scholar 

  51. Ruster, T. et al. A long-lived Zeeman trapped-ion qubit. Appl. Phys. B 122, 254 (2016).

  52. Aharon, N., Spethmann, N., Leroux, I. D., Schmidt, P. O. & Retzker, A. Robust optical clock transitions in trapped ions using dynamical decoupling. New J. Phys. 21, 083040 (2019).

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  PubMed  Article  Google Scholar 

  54. Hughes, A. C. et al. Benchmarking a high-fidelity mixed-species entangling gate. Phys. Rev. Lett. 125, 080504 (2020).

    ADS  CAS  PubMed  Article  Google Scholar 

  55. Boulder Atomic Clock Optical Network (BACON) Collaboration. Frequency ratio measurements at 18-digit accuracy using an optical clock network. Nature 591, 564–569 (2021).

  56. Wright, T. A. et al. Two-way photonic interface for linking the Sr+ transition at 422 nm to the telecommunication C band. Phys. Rev. App. 10, 044012 (2018).

    CAS  Article  Google Scholar 

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We thank E. R. Clements, R. M. Godun, D. B. Hume and A. M. Steane for helpful discussions and insightful comments on the manuscript. We thank Sandia National Laboratories for supplying the HOA2 ion traps used in these experiments. This work was supported by the UK EPSRC Hub in Quantum Computing and Simulation (EP/T001062/1), the EU Quantum Technology Flagship Project AQTION (No. 820495) and C.J.B.’s UKRI Fellowship (MR/S03238X/1). B.C.N. acknowledges funding from the UK National Physical Laboratory.

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Authors and Affiliations



D.P.N., B.C.N., P.D., D.M., G.A., R.S. and C.J.B. built and maintained the experimental apparatus. R.S. conceived the experiments. B.C.N. and R.S. carried out the experiments, assisted by D.P.N., P.D., D.M. and G.A. B.C.N., R.S. and D.M.L. analysed the data. B.C.N. and R.S. wrote the manuscript with input from all authors. C.J.B. and D.M.L. secured funding and supervised the work.

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Correspondence to B. C. Nichol or R. Srinivas.

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C.J.B. is a director of Oxford Ionics. The remaining authors declare no competing interests.

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Nichol, B.C., Srinivas, R., Nadlinger, D.P. et al. An elementary quantum network of entangled optical atomic clocks. Nature 609, 689–694 (2022).

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