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Proton–electron mass ratio by high-resolution optical spectroscopy of ion ensembles in the resolved-carrier regime

Nature Physics volume 17, pages 569–573 (2021)Cite this article

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Abstract

Optical spectroscopy in the gas phase is a key tool for elucidating the structure of atoms and molecules and their interaction with external fields. The line resolution is usually limited by a combination of first-order Doppler broadening due to particle thermal motion and a short transit time through the excitation beam. For trapped particles, suitable laser cooling techniques can lead to strong confinement (the Lamb–Dicke regime) and thus to optical spectroscopy free of these effects. For non-laser-coolable spectroscopy ions, this has so far only been achieved when trapping one or two atomic ions, together with a single laser-coolable atomic ion1,2. Here we show that one-photon optical spectroscopy free of Doppler and transit broadening can also be obtained with more easily prepared ensembles of ions, if performed with mid-infrared radiation. We demonstrate the method on molecular ions. We trap ~100 molecular hydrogen ions (HD+) within a Coulomb cluster of a few thousand laser-cooled atomic ions and perform laser spectroscopy of the fundamental vibrational transition. Transition frequencies were determined with a lowest uncertainty of 3.3 × 10−12 fractionally. As an application, we determine the proton–electron mass ratio by matching a precise ab initio calculation with the measured vibrational frequency.

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Fig. 1: Scheme of the key elements of the apparatus.
Fig. 2: Spectral properties of the mid-infrared laser source.
Fig. 3: Two hyperfine components of the fundamental rovibrational transition of HD+, at a frequency of 58.6 THz.
Fig. 4: Determinations of the ratio of reduced nuclear mass to electron mass \(\mu /{m}_{{\rm{e}}}={m}_{{\rm{e}}}^{-1}{m}_{{\rm{p}}}{m}_{{\rm{d}}}/({m}_{{\rm{p}}}+{m}_{{\rm{d}}})\simeq 1,223.9\).

Data availability

Data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.

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Acknowledgements

We are indebted to E. Wiens for assistance with the frequency comb measurements. We are very grateful to J.-Ph. Karr for communicating the value of \({\mathcal{E}}^{\prime}_1\) before publication. This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant no. 786306, ‘PREMOL’), from the Deutsche Forschungsgemeinschaft (Schi 431/23-1) and from both DFG and the state of Nordrhein-Westfalen via grant no. INST-208/737-1 FUGG. I.V.K. was partly supported by FP7-2013-ITN ‘COMIQ’ (grant no. 607491). V.I.K. acknowledges support from the Russian Foundation for Basic Research under grant no. 19-02-00058-a.

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Authors and Affiliations

  1. Institut für Experimentalphysik, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany

    I. V. Kortunov, S. Alighanbari, M. G. Hansen, G. S. Giri & S. Schiller

  2. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia

    V. I. Korobov

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  1. I. V. Kortunov
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  2. S. Alighanbari
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Contributions

I.V.K., M.G.H. and S.S. developed the laser system. I.V.K., S.A. and G.S.G. performed the experiments and analysed the data. I.V.K., S.S. and V.I.K. performed theoretical calculations. S.S. conceived the study, supervised the work and wrote the manuscript. All authors contributed to editing of the manuscript.

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Correspondence to S. Schiller.

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Supplementary Information

Supplementary Figs. 1–3 and Table 1.

Supplementary Data SI Fig. 2

Numerical data used to generate the graphs in Fig. 2 of the Supplementary Information.

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Numerical data used to generate the graphs in Fig. 3 of the Supplementary Information.

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Source Data Fig. 2

Numerical data used to generate the graphs in Fig. 2 of the main text.

Source Data Fig. 3

Numerical data used to generate the graphs in Fig. 3 of the main text.

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Kortunov, I.V., Alighanbari, S., Hansen, M.G. et al. Proton–electron mass ratio by high-resolution optical spectroscopy of ion ensembles in the resolved-carrier regime. Nat. Phys. 17, 569–573 (2021). https://doi.org/10.1038/s41567-020-01150-7

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