- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Applied

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Active compensation of the ac Stark shift in a two-photon rubidium optical frequency reference using power modulation

Yorick Andeweg1,2,*, John Kitching1, and Matthew T. Hummon1

  • *Contact author: yorick.andeweg@colorado.edu
PDF

Phys. Rev. Applied 25, 034059 – Published 18 March, 2026

DOI: https://doi.org/10.1103/25md-vv43

Abstract

We implement a feedback protocol to suppress the ac Stark shift in a two-photon rubidium optical frequency reference, reducing its sensitivity to optical power variations by a factor of 1000. This method alleviates the tradeoff between short-term and long-term stability imposed by the ac Stark shift, enabling us to simultaneously achieve instabilities of 3×10−14 at 1 s and 2×10−14 at 104 s. We also quantitatively describe, and experimentally explore, a stability limit imposed on clocks using this method by frequency noise on the local oscillator.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (63)

  1. S. Brewer, J.-S. Chen, A. Hankin, E. Clements, C. Chou, D. Wineland, D. Hume, and D. Leibrandt, 27Al+ quantum-logic clock with a systematic uncertainty below 10−18, Phys. Rev. Lett. 123, 033201 (2019).
  2. A. Aeppli, K. Kim, W. Warfield, M. S. Safronova, and J. Ye, Clock with 8×10−19 systematic uncertainty, Phys. Rev. Lett. 133, 023401 (2024).
  3. W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schäffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, Atomic clock performance enabling geodesy below the centimetre level, Nature 564, 87 (2018).
  4. N. Ohmae, M. Takamoto, Y. Takahashi, M. Kokubun, K. Araki, A. Hinton, I. Ushijima, T. Muramatsu, T. Furumiya, Y. Sakai, N. Moriya, N. Kamiya, K. Fujii, R. Muramatsu, T. Shiimado, and H. Katori, Transportable strontiuum optical lattice clocks operated outside laboratory at the level of 10−18 uncertainty, Adv. Quantum Technol. 4, 2100015 (2021).
  5. A. A. Lagatsky, in Emerging Imaging and Sensing Technologies for Security and Defence VIII, Vol. 12740 (SPIE, Amsterdam, the Netherlands, 2023), pp. 90–93.
  6. H. Timmers, B. Sodergren, C. Smith, E. Barnes, A. Spiess, A. Attar, K. Vogel, and K. Knabe, in Quantum Information Science, Sensing, and Computation XVI (SPIE, National Harbor, Maryland, USA, 2024), Vol. 13028, pp. 3–6.
  7. J. Zhang, C. Wang, C. Denney, J. Riemensberger, G. Lihachev, J. Hu, W. Kao, T. Blésin, N. Kuznetsov, Z. Li, M. Churaev, X. Ou, G. Santamaria-Botello, and T. J. Kippenberg, Ultrabroadband integrated electro-optic frequency comb in lithium tantalate, Nature 637, 1096 (2025).
  8. L. A. Hackel, K. H. Casleton, S. G. Kukolich, and S. Ezekiel, Observation of magnetic octupole and scalar spin-spin interactions in I2 using laser spectroscopy, Phys. Rev. Lett. 35, 568 (1975).
  9. J. Ye, L. S. Ma, and J. L. Hall, Molecular iodine clock, Phys. Rev. Lett. 87, 270801 (2001).
  10. J. D. Roslund, A. Cingöz, W. D. Lunden, G. B. Partridge, A. S. Kowligy, F. Roller, D. B. Sheredy, G. E. Skulason, J. P. Song, J. R. Abo-Shaeer, and M. M. Boyd, Optical clocks at sea, Nature 628, 736 (2024).
  11. F. Nez, F. Biraben, R. Felder, and Y. Millerioux, Optical frequency determination of the hyperfine components of the 5S1/2–5D3/2 2-photon transitions in rubidium, Opt. Commun. 102, 432 (1993).
  12. Y. Millerioux, D. Touahri, L. Hilico, A. Clairon, R. Felder, F. Biraben, and B. de Beauvoir, Towards an accurate frequency standard at λ=778nm using a laser diode stabilized on a hyperfine component of the Doppler-free two-photon transitions in rubidium, Opt. Commun. 108, 91 (1994).
  13. T. T. Grove, V. Sanchez-Villicana, B. C. Duncan, S. Maleki, and P. L. Gould, Two-photon two-color diode laser spectroscopy of the Rb 5D5/2 state, Phys. Scr. 52, 271 (1995).
  14. A. Danielli, P. Rusian, A. Arie, M. H. Chou, and M. M. Fejer, Frequency stabilization of a frequency-doubled 1556-nm source to the 5S1/2→5D5/2 two-photon transitions of rubidium, Opt. Lett. 25, 905 (2000).
  15. C. S. Edwards, G. P. Barwood, H. S. Margolis, P. Gill, and W. R. C. Rowley, Development and absolute frequency measurement of a pair of 778 nm two-photon rubidium standards, Metrologia 42, 464 (2005).
  16. J. Wu, D. Hou, Z. Qin, Z. Zhang, and J. Zhao, Observation of Rb two-photon absorption directly excited by an erbium-fiber-laser-based optical frequency comb via spectral control, Phys. Rev. A 89, 041402(R) (2014).
  17. W. Xia, S.-Y. Dai, Y. Zhang, K.-Q. Li, Q. Yu, and X.-Z. Chen, Precision frequency measurement of 87Rb5S1/2(F=2)→5D5/2(F′′=4) two-photon transition through a fiber-based optical frequency comb, Chin. Phys. Lett. 33, 053201 (2016).
  18. O. Terra and H. Hussein, An ultra-stable optical frequency standard for telecommunication purposes based upon the 5S1/2→5D5/2 two-photon transition in rubidium, Appl. Phys. B 122, 27 (2016).
  19. K. W. Martin, G. Phelps, N. D. Lemke, M. S. Bigelow, B. Stuhl, M. Wojcik, M. Holt, I. Coddington, M. W. Bishop, and J. H. Burke, Compact optical atomic clock based on a two-photon transition in rubidium, Phys. Rev. Appl. 9, 014019 (2018).
  20. N. D. Lemke, K. W. Martin, R. Beard, B. K. Stuhl, A. J. Metcalf, and J. D. Elgin, Measurement of optical rubidium clock frequency spanning 65 days, Sensors 22, 1982 (2022).
  21. T. N. Nguyen and T. R. Schibli, Field-programmable gate array-based residual amplitude modulation suppression and control for compact atomic clocks, Rev. Sci. Instrum. 95, 023001 (2024).
  22. S. E. Erickson, D. P. Tooley, K. Weerasinghe, X. Zhu, A. Chavez-Pirson, and R. J. Jones, Atomic frequency standard based on direct frequency comb spectroscopy, Opt. Lett. 49, 5340 (2024).
  23. E. J. Ahern, S. K. Scholten, C. Locke, N. B. Hébert, B. White, A. N. Luiten, and C. Perrella, Tailoring the stability of a two-color, two-photon rubidium frequency standard, Phys. Rev. Appl. 23, 044025 (2025).
  24. B. Cagnac, G. Grynberg, and F. Biraben, Spectroscopie d’absorption multiphotonique sans effet Doppler, J. Phys. 34, 845 (1973).
  25. M. Poulin, C. Latrasse, N. Cyr, and M. Têtu, An absolute frequency reference at 192.6 THz (1556 nm) based on a two-photon absorption line of rubidium at 778 nm for WDM communication systems, IEEE Photonics Technol. Lett. 9, 1631 (1997).
  26. L.-A. Liew, S. Knappe, J. Moreland, H. Robinson, L. Hollberg, and J. Kitching, Microfabricated alkali atom vapor cells, Appl. Phys. Lett. 84, 2694 (2004).
  27. J. H. Burke, N. D. Lemke, G. R. Phelps, and K. W. Martin, A compact, high-performance all optical atomic clock based on telecom lasers, Proc. Int. Soc. Opt. Eng. 9763, 976304 (2016).
  28. Z. L. Newman et al., Architecture for the photonic integration of an optical atomic clock, Optica 6, 680 (2019).
  29. V. Maurice, Z. L. Newman, S. Dickerson, M. Rivers, J. Hsiao, P. Greene, M. Mescher, J. Kitching, M. T. Hummon, and C. Johnson, Miniaturized optical frequency reference for next-generation portable optical clocks, Opt. Express 28, 24708 (2020).
  30. Z. L. Newman, V. Maurice, C. Fredrick, T. Fortier, H. Leopardi, L. Hollberg, S. A. Diddams, J. Kitching, and M. T. Hummon, High-performance, compact optical standard, Opt. Lett. 46, 4702 (2021).
  31. A. P. Hilton, R. F. Offer, E. Klantsataya, S. K. Scholten, N. Bourbeau Hébert, C. J. Billington, C. Locke, C. Perrella, M. Nelligan, J. W. Allison, B. White, E. Ahern, K. W. Martin, R. Beard, J. D. Elgin, B. M. Sparkes, and A. N. Luiten, Demonstration of a mobile optical clock ensemble at sea, Nat. Commun. 16, 6063 (2025).
  32. K. W. Martin, B. Stuhl, J. Eugenio, M. S. Safronova, G. Phelps, J. H. Burke, and N. D. Lemke, Frequency shifts due to Stark effects on a rubidium two-photon transition, Phys. Rev. A 100, 023417 (2019).
  33. D. Li, K. Liu, L. Zhao, and S. Kang, A frequency shift compensation method for light shift and vapor-cell temperature shift in atomic clocks, arXiv:2405.14281.
  34. D. Li, K. Liu, P. Wang, and S. Kang, Dual-interrogation method for suppressing light shift in Rb 778 nm two-photon transition optical frequency standard, Opt. Express 32, 2766 (2024).
  35. R. Blum, S. Kundermann, T. Ruelle, S. Lecomte, and S. Karlen, in Quantum Technologies 2024 (SPIE, 2024), Vol. 12993 pp. 140–142.
  36. V. Gerginov and K. Beloy, Two-photon optical frequency reference with active ac Stark shift cancellation, Phys. Rev. Appl. 10, 014031 (2018).
  37. V. I. Yudin, M. Y. Basalaev, A. V. Taichenachev, J. W. Pollock, Z. L. Newman, M. Shuker, A. Hansen, M. T. Hummon, R. Boudot, E. A. Donley, and J. Kitching, General methods for suppressing the light shift in atomic clocks using power modulation, Phys. Rev. Appl. 14, 024001 (2020).
  38. M. Abdel Hafiz, R. Vicarini, N. Passilly, C. E. Calosso, V. Maurice, J. W. Pollock, A. V. Taichenachev, V. I. Yudin, J. Kitching, and R. Boudot, Protocol for light-shift compensation in a continuous-wave microcell atomic clock, Phys. Rev. Appl. 14, 034015 (2020).
  39. C. Sanner, N. Huntemann, R. Lange, C. Tamm, and E. Peik, Autobalanced Ramsey spectroscopy, Phys. Rev. Lett. 120, 053602 (2018).
  40. M. Abdel Hafiz, G. Coget, M. Petersen, C. Rocher, S. Guérandel, T. Zanon-Willette, E. de Clercq, and R. Boudot, Toward a high-stability coherent population trapping Cs vapor-cell atomic clock using autobalanced Ramsey spectroscopy, Phys. Rev. Appl. 9, 064002 (2018).
  41. M. Abdel Hafiz, G. Coget, M. Petersen, C. E. Calosso, S. Guérandel, E. de Clercq, and R. Boudot, Symmetric autobalanced Ramsey interrogation for high-performance coherent-population-trapping vapor-cell atomic clock, Appl. Phys. Lett. 112, 244102 (2018).
  42. M. Shuker, J. W. Pollock, R. Boudot, V. I. Yudin, A. V. Taichenachev, J. Kitching, and E. A. Donley, Ramsey spectroscopy with displaced frequency jumps, Phys. Rev. Lett. 122, 113601 (2019).
  43. M. Abdel Hafiz, C. Carlé, N. Passilly, J. M. Danet, C. E. Calosso, and R. Boudot, Light-shift mitigation in a microcell-based atomic clock with symmetric auto-balanced Ramsey spectroscopy, Appl. Phys. Lett. 120, 064101 (2022).
  44. M. Arditi and J. L. Picqué, Application of the light-shift effect to laser frequency stabilization with reference to a microwave frequency standard, Opt. Commun. 15, 317 (1975).
  45. M. Hashimoto and M. Ohtsu, A novel method to compensate for the effect of light shift in a rubidium atomic clock pumped by a semiconductor laser, IEEE Trans. Instrum. Meas. 39, 458 (1990).
  46. B. H. McGuyer, Y.-Y. Jau, and W. Happer, Simple method of light-shift suppression in optical pumping systems, Appl. Phys. Lett. 94, 251110 (2009).
  47. C. E. Calosso, M. Gozzelino, F. Levi, and S. Micalizio, Laser-frequency stabilization using light shift in compact atomic clocks, Phys. Rev. Appl. 22, 034033 (2024).
  48. V. Shah, V. Gerginov, P. D. D. Schwindt, S. Knappe, L. Hollberg, and J. Kitching, Continuous light-shift correction in modulated coherent population trapping clocks, Appl. Phys. Lett. 89, 151124 (2006).
  49. V. I. Yudin, M. Yu Basalaev, A. V. Taichenachev, D. A. Radnatarov, V. A. Andryushkov, and S. M. Kobtsev, Method for stabilization of the microwave modulation index in order to suppress the light shift of the coherent population trapping resonances, J. Phys. Conf. Ser. 2067, 012003 (2021).
  50. D. A. Radnatarov, S. M. Kobtsev, V. A. Andryushkov, M. Y. Basalaev, A. V. Taichenachev, M. D. Radchenko, and V. I. Yudin, Active suppression of the light shift in an atomic clock based on coherent population trapping in 87Rb vapor using the phase jump technique, JETP Lett. 117, 504 (2023).
  51. V. I. Yudin, A. V. Taichenachev, M. Y. Basalaev, T. Zanon-Willette, J. W. Pollock, M. Shuker, E. A. Donley, and J. Kitching, Generalized autobalanced Ramsey spectroscopy of clock transitions, Phys. Rev. Appl. 9, 054034 (2018).
  52. M. M. Boyd, A. D. Ludlow, S. Blatt, S. M. Foreman, T. Ido, T. Zelevinsky, and J. Ye, 87Sr lattice clock with inaccuracy below 10−15, Phys. Rev. Lett. 98, 083002 (2007).
  53. See Supplemental Material http://link.aps.org/supplemental/10.1103/25md-vv43 for a derivation of the ACS stability limit, as well as a plot and discussion of our laser’s frequency noise spectrum.
  54. S. Aronson, Reduction of residual amplitude modulation in electro-optic modulators, Bachelor’s thesis (University of Florida, 2020).
  55. H.-Y. Chia, Complex modulation and its applications, Ph.D. thesis (University of Florida, 2022).
  56. J. Rutman and F. L. Walls, Characterization of frequency stability in precision frequency sources, Proc. IEEE 79, 952 (1991).
  57. C. Audoin, V. Candelier, and N. Diamarcq, A limit to the frequency stability of passive frequency standards due to an intermodulation effect, IEEE Trans. Instrum. Meas. 40, 121 (1991).
  58. N. Nader, E. J. Stanton, G. M. Brodnik, N. Jahan, S. C. Weight, L. M. Williams, A. E. Dorche, K. L. Silverman, S. W. Nam, S. B. Papp, and R. P. Mirin, Heterogeneous tantala photonic integrated circuits for sub-micron wavelength applications, Optica 12, 585 (2025).
  59. A. Isichenko, A. S. Hunter, D. Bose, N. Chauhan, M. Song, K. Liu, M. W. Harrington, and D. J. Blumenthal, Sub-Hz fundamental, sub-kHz integral linewidth self-injection locked 780 nm hybrid integrated laser, Sci. Rep. 14, 27015 (2024).
  60. X. Lu, L. Chang, M. A. Tran, T. Komljenovic, J. E. Bowers, and K. Srinivasan, Emerging integrated laser technologies in the visible and short near-infrared regimes, Nat. Photonics 18, 1010 (2024).
  61. E. Di Gaetano, B. Keliehor, K. Gallacher, P. F. Griffin, M. Sorel, E. Riis, and D. J. Paul, 778.1 nm distributed feedback lasers for Rb two-photon atomic systems with sub-4 kHz linewidths, APL Photonics 9, 056114 (2024).
  62. Z. Zhang, B. Shen, M. A. Tran, W. Lee, K. Asawa, G. Kim, Y. Shen, T. J. Morin, A. Malik, J. E. Bowers, T. Komljenovic, and C. Zhang, Photonic integration platform for rubidium sensors and beyond, Optica 10, 752 (2023).
  63. M. A. Tran, C. Zhang, T. J. Morin, L. Chang, S. Barik, Z. Yuan, W. Lee, G. Kim, A. Malik, Z. Zhang, J. Guo, H. Wang, B. Shen, L. Wu, K. Vahala, J. E. Bowers, H. Park, and T. Komljenovic, Extending the spectrum of fully integrated photonics to submicrometre wavelengths, Nature 610, 54 (2022).

Outline

Information

Phys. Rev. Applied 25, 034059– Published 18 March, 2026
  • Received 18 July 2025
  • Revised 30 November 2025
  • Accepted 6 February 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation