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Investigation of the fine structure of antihydrogen

An Author Correction to this article was published on 18 May 2021

This article has been updated


At the historic Shelter Island Conference on the Foundations of Quantum Mechanics in 1947, Willis Lamb reported an unexpected feature in the fine structure of atomic hydrogen: a separation of the 2S1/2 and 2P1/2 states1. The observation of this separation, now known as the Lamb shift, marked an important event in the evolution of modern physics, inspiring others to develop the theory of quantum electrodynamics2,3,4,5. Quantum electrodynamics also describes antimatter, but it has only recently become possible to synthesize and trap atomic antimatter to probe its structure. Mirroring the historical development of quantum atomic physics in the twentieth century, modern measurements on anti-atoms represent a unique approach for testing quantum electrodynamics and the foundational symmetries of the standard model. Here we report measurements of the fine structure in the n = 2 states of antihydrogen, the antimatter counterpart of the hydrogen atom. Using optical excitation of the 1S–2P Lyman-α transitions in antihydrogen6, we determine their frequencies in a magnetic field of 1 tesla to a precision of 16 parts per billion. Assuming the standard Zeeman and hyperfine interactions, we infer the zero-field fine-structure splitting (2P1/2–2P3/2) in antihydrogen. The resulting value is consistent with the predictions of quantum electrodynamics to a precision of 2 per cent. Using our previously measured value of the 1S–2S transition frequency6,7, we find that the classic Lamb shift in antihydrogen (2S1/2–2P1/2 splitting at zero field) is consistent with theory at a level of 11 per cent. Our observations represent an important step towards precision measurements of the fine structure and the Lamb shift in the antihydrogen spectrum as tests of the charge–parity–time symmetry8 and towards the determination of other fundamental quantities, such as the antiproton charge radius9,10, in this antimatter system.

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Fig. 1: Expected antihydrogen energy levels.
Fig. 2: The ALPHA-2 central apparatus.
Fig. 3: 1S–2P fine-structure spectrum of antihydrogen.
Fig. 4: Comparison of antihydrogen and hydrogen transition frequencies.

Data availability

The datasets generated and/or analysed during the current study are available from J.S.H. on reasonable request.

Change history


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This work was supported by: the European Research Council through its Advanced Grant programme (J.S.H.); CNPq, FAPERJ, RENAFAE (Brazil); NSERC, ALPHA-g/CRUCS CFI, NRC/TRIUMF, EHPDS/EHDRS (Canada); FNU (Nice Centre), Carlsberg Foundation (Denmark); ISF (Israel); STFC, EPSRC, the Royal Society and the Leverhulme Trust (UK); DOE, NSF (USA); and VR (Sweden). We are grateful for the efforts of the CERN AD team, without which these experiments could not have taken place. We thank P. Djuricanin (University of British Columbia) for extensive help with the laser system and calibrations. We thank J. Tonoli and the CERN staff, as well as T. Mittertreiner and the UBC staff, for extensive, time-critical help with machining and electrical works. We thank the staff of the Superconducting Magnet Division at Brookhaven National Laboratory for collaboration and for the fabrication of the trapping magnets. We thank C. Marshall (TRIUMF) for work on the ALPHA-2 cryostat. We thank F. Besenbacher (Aarhus) for timely support in procuring the ALPHA-2 external solenoid. We thank T. Miller (Ohio) for advice on the initial development of the pulsed laser system. We thank A. Kostelecky and G. Drake for discussions on the theoretical aspects of this work.

Author information




This study was based on data collected using the ALPHA-2 antihydrogen trapping apparatus, designed and constructed by the ALPHA Collaboration using methods developed by the entire collaboration. The entire collaboration participated in the operation of the apparatus and the data-taking activities. Pulsed Lyman-α spectroscopy was first proposed by M.C.F. and developed further by T.M., F.R., J.M.M., R.C., A.E., A.K. and M.C.F. The original laser was designed by T.M. and tested by J.M.M. and T.M. The laser system at CERN was implemented, commissioned and operated by J.M.M., R.C., A.E., A.K. and T.M. The simulation program for laser interaction with magnetically trapped atoms was developed by F.R. The microwave techniques and ECR magnetometry were developed by T.F., M.E.H. and W.N.H. The positron accumulator is the responsibility of C.J.B., M.C., M.S., C.A.I. and D.P.v.d.W. The annihilation detector system was developed by A.C., M.C.F., D.R.G., L.K., J.T.K.M., S.M., K.O., A.O. and P.P. Detailed analysis of the antiproton annihilation detector data was done by J.T.K.M., A.E. and A.O. The frequency determination and the evaluation of its uncertainty was performed by T.M., M.C.F., A.K., A.E., R.C., R.I.T. and A.O. The manuscript was written by T.M., M.C.F. and J.S.H., with significant input from A.K., R.C., A.E., A.O., J.T.K.M., M.E.H., N.M., C.Ø.R. and F.R. The manuscript was edited and improved by the entire collaboration.

Corresponding authors

Correspondence to M. C. Fujiwara or J. S. Hangst or T. Momose.

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Extended data figures and tables

Extended Data Fig. 1 Determination of transition frequencies.

ad, For each series, the experimental data (filled black circles with error bars) are plotted with fits of various models (red lines) discussed in Methods. The experimental data are normalized to the total number of the detected antihydrogen atoms and a laser power of 5 nW. Also shown are the results of standard simulations (open blue squares with error bars), similarly normalized to the total number of simulated atoms, illustrating the degree of agreement between the data and the simulations, without any tuning parameters. Some discrepancies in the amplitudes can be observed, which may point to errors in our laser power estimates. We note that because our frequency-fitting procedure allows variations in the relative amplitudes, the fits are largely insensitive to the amplitude differences (Methods). Error bars represent 1σ.

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The ALPHA Collaboration. Investigation of the fine structure of antihydrogen. Nature 578, 375–380 (2020).

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