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Real-time phase tracking for wide-band optical frequency measurements at the 20th decimal place


Optical frequency measurements are among the most precise tools available to science. With the rapid advances in optical clocks now achieving a low 10−17 stability at 1 s and averaging down to the 10−19 level in a few hundred seconds, real-time sensing of subtle phenomena becomes essential. To render possible such measurements, we introduce real-time optical phase tracking with ultra-low-noise frequency combs as a fundamental means to constantly monitor frequency offsets. This enables the characterization of optical frequency synthesis with stability and accuracy at the 20th decimal place within a measurement time of <100 s. To enable comb operation at this level of performance, dichroic heterodyne detection is used to compensate phase drifts occurring in the generation and dissemination of widely spaced optical frequencies. We qualify an example set-up by comparison with a reference system, measuring an offset between two combs of (5.4 ± 5.3) × 10−21 in one single measurement run of 1 × 105 s.

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Fig. 1: Schematic of dichroic heterodyne detection for phase drift compensation.
Fig. 2: Experimental set-up.
Fig. 3: Phase noise and phase tracking of the uncompensated heterodyne beat notes.
Fig. 4: Phase tracking and fractional frequency instability employing dichroic heterodyne detection.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.


  1. 1.

    Hall, J. L. Nobel lecture: Defining and measuring optical frequencies. Rev. Mod. Phys. 78, 1279–1295 (2006).

    ADS  Article  Google Scholar 

  2. 2.

    Hänsch, T. W. Nobel lecture: Passion for precision. Rev. Mod. Phys. 78, 1297–1309 (2006).

    ADS  Article  Google Scholar 

  3. 3.

    Udem, T., Reichert, J., Holzwarth, R. & Hänsch, T. W. Absolute optical frequency measurement of the cesium D1 line with a mode-locked laser. Phys. Rev. Lett. 82, 3568–3571 (1999).

    ADS  Article  Google Scholar 

  4. 4.

    Diddams, S. A. et al. Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb. Phys. Rev. Lett. 84, 5102–5105 (2000).

    ADS  Article  Google Scholar 

  5. 5.

    Udem, T., Holzwarth, R. & Hänsch, T. W. Optical frequency metrology. Nature 416, 233–237 (2002).

    ADS  Article  Google Scholar 

  6. 6.

    Keilmann, F., Gohle, C. & Holzwarth, R. Time-domain mid-infrared frequency-comb spectrometer. Opt. Lett. 29, 1542–1544 (2004).

    ADS  Article  Google Scholar 

  7. 7.

    Barmes, I., Witte, S. & Eikema, K. S. E. Spatial and spectral coherent control with frequency combs. Nat. Photon. 7, 38–42 (2013).

    ADS  Article  Google Scholar 

  8. 8.

    Bernhardt, B. et al. Cavity-enhanced dual-comb spectroscopy. Nat. Photon. 4, 55–57 (2010).

    ADS  Article  Google Scholar 

  9. 9.

    Coddington, I., Newbury, N. & Swann, W. Dual-comb spectroscopy. Optica 3, 414–426 (2016).

    ADS  Article  Google Scholar 

  10. 10.

    Lomsadze, B., Smith, B. C. & Cundiff, S. T. Tri-comb spectroscopy. Nat. Photon. 12, 676–680 (2018).

    ADS  Article  Google Scholar 

  11. 11.

    Picqué, N. & Hänsch, T. W. Frequency comb spectroscopy. Nat. Photon. 13, 146–157 (2019).

    ADS  Article  Google Scholar 

  12. 12.

    Baltuška, A. et al. Attosecond control of electronic processes by intense light fields. Nature 421, 611–615 (2003).

    ADS  Article  Google Scholar 

  13. 13.

    Fortier, T. M. et al. Generation of ultrastable microwaves via optical frequency division. Nat. Photon. 5, 425–429 (2011).

    ADS  Article  Google Scholar 

  14. 14.

    Xie, X. et al. Photonic microwave signals with zeptosecond-level absolute timing noise. Nat. Photon. 11, 44–47 (2016).

    ADS  Article  Google Scholar 

  15. 15.

    Zobel, J. W. et al. Comparison of optical frequency comb and sapphire loaded cavity microwave oscillators. IEEE Photon. Technol. Lett. 31, 1323–1326 (2019).

    ADS  Article  Google Scholar 

  16. 16.

    Coddington, I., Swann, W. C., Nenadovic, L. & Newbury, N. R. Rapid and precise absolute distance measurements at long range. Nat. Photon. 3, 351–356 (2009).

    ADS  Article  Google Scholar 

  17. 17.

    Lezius, M. et al. Space-borne frequency comb metrology. Optica 3, 1381–1387 (2016).

    ADS  Article  Google Scholar 

  18. 18.

    Diddams, S. A. et al. An optical clock based on a single trapped 199Hg+ ion. Science 293, 825–828 (2001).

    ADS  Article  Google Scholar 

  19. 19.

    Udem, Th., Holzwarth, R. & Hänsch, T. W. Optical frequency metrology. Nature 416, 233–237 (2002).

    ADS  Article  Google Scholar 

  20. 20.

    Schioppo, M. et al. Ultrastable optical clock with two cold-atom ensembles. Nat. Photon. 11, 48–52 (2017).

    ADS  Article  Google Scholar 

  21. 21.

    Campbell, S. L. et al. A Fermi-degenerate three-dimensional optical lattice clock. Science 358, 90–94 (2017).

    ADS  Article  Google Scholar 

  22. 22.

    Marti, G. E. et al. Imaging optical frequencies with 100 µHz precision and 1.1 µm resolution. Phys. Rev. Lett. 120, 103201 (2017).

    ADS  Article  Google Scholar 

  23. 23.

    Ushijima, I., Takamoto, M., Das, M., Ohkubo, T. & Katori, H. Cryogenic optical lattice clocks. Nat. Photon. 9, 185–189 (2015).

    ADS  Article  Google Scholar 

  24. 24.

    Nicholson, T. L. et al. Systematic evaluation of an atomic clock at 2 × 10−18 total uncertainty. Nat. Commun. 6, 6896 (2015).

    ADS  Article  Google Scholar 

  25. 25.

    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).

    ADS  Article  Google Scholar 

  26. 26.

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

    ADS  Article  Google Scholar 

  27. 27.

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

    ADS  Article  Google Scholar 

  28. 28.

    Kessler, T. et al. A sub-40-mHz-linewidth laser based on a silicon single-crystal optical cavity. Nat. Photon. 6, 687–692 (2012).

    ADS  Article  Google Scholar 

  29. 29.

    Häfner, S. et al. 8 × 10−17 fractional laser frequency instability with a long room-temperature cavity. Opt. Lett. 40, 2112–2115 (2015).

    ADS  Article  Google Scholar 

  30. 30.

    Matei, D. G. et al. 1.5 μm lasers with sub-10 mHz linewidth. Phys. Rev. Lett. 118, 263202 (2017).

    ADS  Article  Google Scholar 

  31. 31.

    Robinson, J. M. et al. Crystalline optical cavity at 4 K with thermal-noise-limited instability and ultralow drift. Optica 6, 240–243 (2019).

    ADS  Article  Google Scholar 

  32. 32.

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

    ADS  Article  Google Scholar 

  33. 33.

    Takano, T. et al. Geopotential measurements with synchronously linked optical lattice clocks. Nat. Photon. 10, 662–666 (2016).

    ADS  Article  Google Scholar 

  34. 34.

    Grotti, J. et al. Geodesy and metrology with a transportable optical clock. Nat. Phys. 14, 437–441 (2018).

    Article  Google Scholar 

  35. 35.

    Takamoto, M. et al. Frequency ratios of Sr, Yb and Hg based optical lattice clocks and their applications. C. R. Phys. 16, 489–498 (2015).

    Article  Google Scholar 

  36. 36.

    Nemitz, N. et al. Frequency ratio of Yb and Sr clocks with 5 × 10−17 uncertainty at 150 seconds averaging time. Nat. Photon. 10, 258–261 (2016).

    ADS  Article  Google Scholar 

  37. 37.

    Ma, L. et al. Optical frequency synthesis and comparison with uncertainty at the 10−19 level. Science 303, 1843–1845 (2004).

    ADS  Article  Google Scholar 

  38. 38.

    Nicolodi, D. et al. Spectral purity transfer between optical wavelengths at the 10−18 level. Nat. Photon. 8, 219–223 (2014).

    ADS  Article  Google Scholar 

  39. 39.

    Johnson, L. A. M., Gill, P. & Margolis, H. S. Evaluating the performance of the NPL femtosecond frequency combs: agreement at the 10−21 level. Metrologia 52, 62–71 (2015).

    ADS  Article  Google Scholar 

  40. 40.

    Yao, Y., Jiang, Y., Yu, H., Bi, Z. & Ma, L. Optical frequency divider with division uncertainty at the 10−21 level. Natl Sci. Rev. 3, 463–469 (2016).

    Google Scholar 

  41. 41.

    Leopardi, H. et al. Single-branch Er:fiber frequency comb for precision optical metrology with 10−18 fractional instability. Optica 4, 879–885 (2017).

    ADS  MathSciNet  Article  Google Scholar 

  42. 42.

    Rolland, A. et al. Ultra-broadband dual-branch optical frequency comb with 10−18 instability. Optica 5, 1070–1077 (2018).

    ADS  Article  Google Scholar 

  43. 43.

    Barbieri, P., Clivati, C., Pizzocaro, M., Levi, F. & Calonico, D. Spectral purity transfer with 5 × 10−17 instability at 1 s using a multibranch Er:fiber frequency comb. Metrologia 56, 045008 (2019).

    Article  Google Scholar 

  44. 44.

    Telle, H. R., Lipphardt, B. & Stenger, J. Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements. Appl. Phys. B 74, 1–6 (2002).

    ADS  Article  Google Scholar 

  45. 45.

    Santarelli, G. et al. Frequency stability degradation of an oscillator slaved to a periodically interrogated atomic resonator. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 887–894 (1998).

    Article  Google Scholar 

  46. 46.

    Marra, G., Margolis, H. S. & Richardson, D. J. Dissemination of an optical frequency comb over fiber with 3 × 10−18 fractional accuracy. Opt. Express 20, 1775–1782 (2012).

    ADS  Article  Google Scholar 

  47. 47.

    Riehle, F. Towards a redefinition of the second based on optical atomic clocks. C. R. Phys. 16, 506–515 (2015).

    Article  Google Scholar 

  48. 48.

    Grebing, C. et al. Realization of a timescale with an accurate optical lattice clock. Optica 3, 563–569 (2016).

    ADS  Article  Google Scholar 

  49. 49.

    Riehle, F. Optical clock networks. Nat. Photon. 11, 25–31 (2017).

    ADS  Article  Google Scholar 

  50. 50.

    Bize, S. The unit of time: present and future directions. C. R. Phys. 20, 153–168 (2019).

    ADS  Article  Google Scholar 

  51. 51.

    Milner, W. R. et al. Demonstration of a time scale based on a stable optical carrier. Phys. Rev. Lett. (in the press); preprint at (2019).

  52. 52.

    Hänsel, W. et al. All polarization-maintaining fiber laser architecture for robust femtosecond pulse generation. Appl. Phys. B 123, 41 (2017).

    ADS  Article  Google Scholar 

  53. 53.

    Hänsel, W., Giunta, M., Lezius, M., Fischer, M. & Holzwarth, R. Electro-optic modulator for rapid control of the carrier-envelope offset frequency. In Conference on Lasers and Electro-Optics SF1C.5 (OSA, 2017).

  54. 54.

    Nazarova, T., Riehle, F. & Sterr, U. Vibration-insensitive reference cavity for an ultra-narrow-linewidth laser. Appl. Phys. B 83, 531–536 (2006).

    ADS  Article  Google Scholar 

  55. 55.

    Kramer, G. & Klische, W. Extra high precision digital phase recorder. In 18th European Frequency and Time Forum 595–602 (Institution of Engineering and Technology, 2004).

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We acknowledge funding from the European Union’s 7th Framework Programme (EU FP7) Marie Skłodowska-Curie Initial Training Network Future Atomic Clock Technology (FACT), the Defense Advanced Research Projects Agency’s (DARPA) Program in Ultrafast Laser Science and Engineering (PULSE, PμreComb project) under contract no. W31P4Q-14-C-0050 and the German Space Agency (DLR) projects ‘Faser-optischer Kammgenerator für angewandte LIDAR-Spektroskopie’ (FOKAL), ‘Faser-optischer Kammgenerator unter Schwerelosigkeit’ (FOKUS and FOKUS II) and ‘InfraRed Astronomy Satellite Swarm Interferometry’ (IRASSI). We thank H. Katori and J. Ye for insightful discussions and colleagues from Menlo Systems for technical support.

Author information




M.G. and W.H. performed the experiments, conceived and realized the two frequency combs and the optical set-up. M.G. analysed the data. M.G. and W.H. wrote the manuscript. M.F. and M.L. managed the project. T.U. provided deep insight into the interpretation of the results and aided with the optical set-up. R.H. initiated and led the activities. All co-authors commented on and improved the manuscript.

Corresponding author

Correspondence to Michele Giunta.

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Giunta, M., Hänsel, W., Fischer, M. et al. Real-time phase tracking for wide-band optical frequency measurements at the 20th decimal place. Nat. Photonics 14, 44–49 (2020).

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