Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Two-photon laser spectroscopy of antiprotonic helium and the antiproton-to-electron mass ratio


Physical laws are believed to be invariant under the combined transformations of charge, parity and time reversal (CPT symmetry1). This implies that an antimatter particle has exactly the same mass and absolute value of charge as its particle counterpart. Metastable antiprotonic helium (He+) is a three-body atom2 consisting of a normal helium nucleus, an electron in its ground state and an antiproton () occupying a Rydberg state with high principal and angular momentum quantum numbers, respectively n and l, such that n ≈ l + 1 ≈ 38. These atoms are amenable to precision laser spectroscopy, the results of which can in principle be used to determine the antiproton-to-electron mass ratio and to constrain the equality between the antiproton and proton charges and masses. Here we report two-photon spectroscopy of antiprotonic helium, in which 3He+ and 4He+ isotopes are irradiated by two counter-propagating laser beams. This excites nonlinear, two-photon transitions of the antiproton of the type (n, l) → (n − 2, l − 2) at deep-ultraviolet wavelengths (λ = 139.8, 193.0 and 197.0 nm), which partly cancel the Doppler broadening of the laser resonance caused by the thermal motion of the atoms. The resulting narrow spectral lines allowed us to measure three transition frequencies with fractional precisions of 2.3–5 parts in 109. By comparing the results with three-body quantum electrodynamics calculations, we derived an antiproton-to-electron mass ratio of 1,836.1526736(23), where the parenthetical error represents one standard deviation. This agrees with the proton-to-electron value known to a similar precision.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Energy levels, Cherenkov detector signals and experimental layout for two-photon spectroscopy of He+.
Figure 2: Profiles of sub-Doppler two-photon resonances.
Figure 3: Two-photon transition frequencies.
Figure 4: Antiproton-to-electron and proton-to-electron mass ratios.


  1. Bluhm, R., Kostelecký, V. A. & Russell, N. CPT and Lorentz tests in hydrogen and antihydrogen. Phys. Rev. Lett. 82, 2254–2257 (1999)

    Article  ADS  CAS  Google Scholar 

  2. Hayano, R. S., Hori, M., Horváth, D. & Widmann, E. Testing CPT invariance with antiprotonic helium. Rep. Prog. Phys. 70, 1995–2065 (2007)

    Article  ADS  CAS  Google Scholar 

  3. Korobov, V. I. Calculations of transitions between metastable states of antiprotonic helium including relativistic and radiative corrections of order R∞α4 . Phys. Rev. A 77, 042506 (2008)

    Article  ADS  Google Scholar 

  4. Hori, M. et al. Direct measurement of transition frequencies in isolated He+ atoms, and new CPT-violation limits on the antiproton charge and mass. Phys. Rev. Lett. 91, 123401 (2003)

    Article  ADS  CAS  Google Scholar 

  5. Hori, M. et al. Determination of the antiproton-to-electron mass ratio by precision laser spectroscopy of He+ . Phys. Rev. Lett. 96, 243401 (2006)

    Article  ADS  CAS  Google Scholar 

  6. Parthey, C. G. et al. Precision measurement of the hydrogen-deuterium 1s-2s isotope shift. Phys. Rev. Lett. 104, 233001 (2010)

    Article  ADS  Google Scholar 

  7. Gabrielse, G. et al. Antihydrogen production within a Penning-Ioffe trap. Phys. Rev. Lett. 100, 113001 (2008)

    Article  ADS  CAS  Google Scholar 

  8. Andresen, G. B. et al. Trapped antihydrogen. Nature 468, 673–676 (2010)

    Article  ADS  CAS  Google Scholar 

  9. Hori, M. & Korobov, V. I. Calculation of transition probabilities and ac Stark shifts in two-photon laser transitions of antiprotonic helium. Phys. Rev. A 81, 062508 (2010)

    Article  ADS  Google Scholar 

  10. Bjorkholm, J. E. & Liao, P. F. Resonant enhancement of two-photon absorption in sodium vapor. Phys. Rev. Lett. 33, 128–131 (1974)

    Article  ADS  CAS  Google Scholar 

  11. Hori, M. & Dax, A. Chirp-corrected, nanosecond Ti:sapphire laser with 6 MHz linewidth for spectroscopy of antiprotonic helium. Opt. Lett. 34, 1273–1275 (2009)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  13. Meyer, V. et al. Measurement of the 1s-2s energy interval in muonium. Phys. Rev. Lett. 84, 1136–1139 (2000)

    Article  ADS  CAS  Google Scholar 

  14. Eikema, K. S. E., Ubachs, W., Vassen, W. & Hogervorst, W. Lamb shift measurement in the 11S ground state of helium. Phys. Rev. A 55, 1866–1884 (1997)

    Article  ADS  CAS  Google Scholar 

  15. Bakule, P. et al. A chirp-compensated, injection-seeded alexandrite laser. Appl. Phys. B 71, 11–17 (2000)

    Article  ADS  CAS  Google Scholar 

  16. Korobov, V. I. Hyperfine structure of metastable states in 3He+ . Phys. Rev. A 73, 022509 (2006)

    Article  ADS  Google Scholar 

  17. Bakalov, D., Jeziorski, B., Korona, T. & Szalewicz, K. &. Tchoukova, E. Density shift and broadening of transition lines in antiprotonic helium. Phys. Rev. Lett. 84, 235–238 (2000)

    Article  ADS  Google Scholar 

  18. Hori, M. et al. Sub-ppm laser spectroscopy of antiprotonic helium and a CPT-violation limit on the antiprotonic charge and mass. Phys. Rev. Lett. 87, 093401 (2001)

    Article  ADS  CAS  Google Scholar 

  19. Mohr, P. J. & Taylor, B. N. CODATA recommended values of the fundamental constants: 2002. Rev. Mod. Phys. 77, 1–107 (2005)

    Article  ADS  CAS  Google Scholar 

  20. Pohl, R. et al. The size of the proton. Nature 466, 213–216 (2010)

    Article  ADS  CAS  Google Scholar 

  21. Van Dyck, R. S., Jr Moore, F. L., Farnham, D. L. & Schwinberg, P. B. Improved measurement of proton-electron mass ratio. Bull. Am. Phys. Soc. 31, 244–244 (1986)

    Google Scholar 

  22. Farnham, D. L., Van Dyck, R. S., Jr & Schwinberg, P. B. Determination of the electron’s atomic mass and the proton/electron mass ratio via Penning trap mass spectroscopy. Phys. Rev. Lett. 75, 3598–3601 (1995)

    Article  ADS  CAS  Google Scholar 

  23. Beier, T. et al. New determination of the electron’s mass. Phys. Rev. Lett. 88, 011603 (2002)

    Article  ADS  Google Scholar 

  24. Verdú, J. et al. Electronic g factor of hydrogenlike oxygen 16O7+ . Phys. Rev. Lett. 92, 093002 (2004)

    Article  ADS  Google Scholar 

  25. Koelemeij, J. C. J., Roth, B., Wicht, A. & Ernsting, I. &. Schiller, S. Variational spectroscopy of HD+ with 2-ppb accuracy. Phys. Rev. Lett. 98, 173002 (2007)

    Article  ADS  Google Scholar 

  26. Hughes, R. J. & Deutch, B. I. Electric charges of positrons and antiprotons. Phys. Rev. Lett. 69, 578–581 (1992)

    Article  ADS  CAS  Google Scholar 

  27. Nakamura, K. et al. Review of particle physics. J. Phys. G 37, 075021 (2010)

    Article  ADS  Google Scholar 

  28. Gabrielse, G. et al. Precision mass spectroscopy of the antiproton and proton using simultaneously trapped particles. Phys. Rev. Lett. 82, 3198–3201 (1999)

    Article  ADS  CAS  Google Scholar 

  29. Thompson, J. K., Rainville, S. & Pritchard, D. E. Cyclotron frequency shifts arising from polarization forces. Nature 430, 58–61 (2004)

    Article  ADS  CAS  Google Scholar 

  30. Fendel, P., Bergeson, S. D., Udem & Hänsch, T. W. Two-photon frequency comb spectroscopy of the 6s-8s transition in cesium. Opt. Lett. 32, 701–703 (2007)

    Article  ADS  CAS  Google Scholar 

Download references


This work was supported by the European Science Foundation (EURYI), Monbukagakusho (grant no. 20002003), the Munich Advanced Photonics cluster of the Deutsche Forschungsgemeinschaft, the Hungarian Research Foundation (K72172) and the Austrian Federal Ministry of Science and Research. We thank the CERN Antiproton Decelerator and Proton Synchrotron operational staff, the CERN cryogenics laboratory, J. Alnis, D. Bakalov, J. Eades, R. Holzwarth, V. I. Korobov, M. Mitani, W. Pirkl and T. Udem.

Author information

Authors and Affiliations



M.H. designed the two-photon experiment. M.H. and A.D. developed the laser systems and carried out the caesium and rubidium measurements. M.H. and D.B. constructed the cryogenic target. M.H. developed the antiproton beam profile monitors, Cherenkov counters, cryogenic optics and data acquisition system. D.B. and M.H. wrote the analysis software. All authors contributed to the beam-time data taking and analysis. M.H. wrote the manuscript and all authors discussed the results and contributed to the editing.

Corresponding author

Correspondence to Masaki Hori.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Hori, M., Sótér, A., Barna, D. et al. Two-photon laser spectroscopy of antiprotonic helium and the antiproton-to-electron mass ratio. Nature 475, 484–488 (2011).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing