Skip to main content

Thank you for visiting nature.com. 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.

  • Article
  • Published:

Test of charged baryon interaction with high-resolution vibrational spectroscopy of molecular hydrogen ions

Nature Physics volume 19, pages 1263–1269 (2023)Cite this article

Subjects

Abstract

Molecular hydrogen ions are of high interest in fundamental physics and metrology. In particular, the long-range baryon–baryon interaction and the degrees of freedom of baryon rotational and vibrational motion are key features of molecular hydrogen ions. Here we present the measurement of a one-photon transition of HD+, a fourth overtone vibrational transition. Through a comparison of experimental and ab initio frequencies of this and previously measured transitions, we implement a test of the low-energy quantum physics of baryon interaction and motion. The results may also be interpreted as a test of Weinberg’s quantum mechanics extension. Furthermore, we compare the value of the fundamental constant combination μ/me = mpmd/(mp + md)me determined from our measurement with the value obtained from mass spectrometry experiments. This may also be regarded as a test of the quantum behaviour of baryons, revealing a moderate tension of 1.7 times the combined uncertainty. Combining our measurement result with some previous ones on HD+, we obtain a least-squares-adjusted value for μ/me as well as a bound for the force between the proton and deuteron in a scenario that is beyond the Standard Model of particle physics. No evidence of a deviation from conventional quantum physics is found.

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

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Selected states of HD+ and transitions relevant to this work.
Fig. 2: Two hyperfine components at f5 ≃ 260 THz, measured under different operating conditions.
Fig. 3: Bounds to the strength of a BSM proton–deuteron Yukawa-type interaction.

Similar content being viewed by others

Data availability

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

Code availability

No custom code or software was used for analysis and presentation of the data associated with this paper.

References

  1. Caswell, W. & Lepage, G. Effective Lagrangians for bound state problems in QED, QCD, and other field theories. Phys. Lett. B 167, 437–442 (1986).

    Article  ADS  Google Scholar 

  2. Korobov, V. I. & Karr, J.-P. Rovibrational spin-averaged transitions in the hydrogen molecular ions. Phys. Rev. A 104, 032806 (2021).

    Article  ADS  MathSciNet  Google Scholar 

  3. Alighanbari, S., Giri, G. S., Constantin, F. L., Korobov, V. I. & Schiller, S. Precise test of quantum electrodynamics and determination of fundamental constants with HD+ ions. Nature 581, 152–158 (2020).

    Article  Google Scholar 

  4. Kortunov, I. V. et al. Proton–electron mass ratio by high-resolution optical spectroscopy of ion ensembles in the resolved-carrier regime. Nat. Phys. 17, 59–573 (2021).

    Article  Google Scholar 

  5. Germann, M. et al. Three-body QED test and fifth-force constraint from vibrations and rotations of HD+. Phys. Rev. Research 3, L022028 (2021).

    Article  ADS  Google Scholar 

  6. Weinberg, S. Lindblad decoherence in atomic clocks. Phys. Rev. A 94, 042117 (2016).

    Article  ADS  Google Scholar 

  7. Blythe, P., Roth, B., Fröhlich, U., Wenz, H. & Schiller, S. Production of ultracold trapped molecular hydrogen ions. Phys. Rev. Lett. 95, 183002 (2005).

    Article  ADS  Google Scholar 

  8. Hornekær, L., Kjærgaard, N., Thommesen, A. M. & Drewsen, M. Structural properties of two-component Coulomb crystals in linear Paul traps. Phys. Rev. Lett. 86, 1994–1997 (2001).

    Article  ADS  Google Scholar 

  9. Kondov, S. S. et al. Molecular lattice clock with long vibrational coherence. Nat. Phys. 15, 1118–1122 (2019).

    Article  Google Scholar 

  10. Amitay, Z., Zajfman, D. & Forck, P. Rotational and vibrational lifetime of isotopically asymmetrized homonuclear diatomic molecular ions. Phys. Rev. A 50, 2304–2308 (1994).

    Article  ADS  Google Scholar 

  11. Karr, J.-P., Haidar, M., Hilico, L., Zhong, Z.-X. & Korobov, V. I. Higher-order corrections to spin-spin scalar interactions in HD+ and \({{{{\rm{H}}}}}_{2}^{+}\). Phys. Rev. A 102, 052827 (2020).

    Article  ADS  Google Scholar 

  12. Korobov, V. I., Karr, J.-P., Haidar, M. & Zhong, Z.-X. Hyperfine structure in the \({{{{\rm{H}}}}}_{2}^{+}\) and HD+ molecular ions at order mα6. Phys. Rev. A 102, 022804 (2020).

    Article  ADS  Google Scholar 

  13. Korobov, V. I. & Karr, J.-P. Spin–orbit interaction in the HD+ ion. Eur. Phys. J. D 76, 197 (2022).

    Article  ADS  Google Scholar 

  14. Tiesinga, E., Mohr, P. J., Newell, D. B. & Taylor, B. N. CODATA recommended values of the fundamental physical constants: 2018. Rev. Mod. Phys. 93, 025010 (2021).

    Article  ADS  Google Scholar 

  15. Haidar, M., Korobov, V. I., Hilico, L. & Karr, J.-P. Higher-order corrections to the spin-orbit and spin-spin tensor interactions in HD+. Phys. Rev. A 106, 042815 (2022).

    Article  ADS  Google Scholar 

  16. Raizen, M. G., Gilbert, G. & Budker, D. Proposed test of quantum mechanics with three connected atomic clock transitions. Phys. Rev. A 106, 032209 (2022).

    Article  ADS  Google Scholar 

  17. Karr, J.-P.\({{{{\rm{H}}}}}_{2}^{+}\) and HD+ : candidates for a molecular clock. J. Mol. Spectrosc. 300, 37–43 (2014).

    Article  Google Scholar 

  18. Schiller, S., Bakalov, D. & Korobov, V. I. Simplest molecules as candidates for precise optical clocks. Phys. Rev. Lett. 113, 023004 (2014).

    Article  ADS  Google Scholar 

  19. Bakalov, D. & Schiller, S. The electric quadrupole moment of molecular hydrogen ions and their potential for a molecular ion clock. Appl. Phys. B 114, 213–230 (2014).

    Article  ADS  Google Scholar 

  20. Korobov, V. I., Danev, P., Bakalov, D. & Schiller, S. Laser-stimulated electric quadrupole transitions in the molecular hydrogen ion H\({}_{2}^{+}\). Phys. Rev. A 97, 032505 (2018).

    Article  ADS  Google Scholar 

  21. Köhler, F. et al. The electron mass from g-factor measurements on hydrogen-like carbon 12C5+. J. Phys. B: At. Mol. Opt. Phys. 48, 144032 (2015).

    Article  ADS  Google Scholar 

  22. Heiße, F. et al. High-precision mass spectrometer for light ions. Phys. Rev. A 100, 022518 (2019).

    Article  ADS  Google Scholar 

  23. Rau, S. et al.Penning trap mass measurements of the deuteron and the HD+ molecular ion. Nature 585, 43–47 (2020).

    Article  ADS  Google Scholar 

  24. Fink, D. J. & Myers, E. G.Deuteron-to-proton mass ratio from simultaneous measurement of the cyclotron frequencies of H\({}_{2}^{+}\) and D+. Phys. Rev. Lett. 127, 243001 (2021).

    Article  ADS  Google Scholar 

  25. Salumbides, E., Ubachs, W. & Korobov, V. Bounds on fifth forces at the sub-Å length scale. J. Mol. Spectrosc. 300, 65–69 (2014).

    Article  Google Scholar 

  26. Czachorowski, P., Puchalski, M., Komasa, J. & Pachucki, K. Nonadiabatic relativistic correction in H2, D2, and HD. Phys. Rev. A 98, 052506 (2018).

    Article  ADS  Google Scholar 

  27. Morel, L., Yao, Z., Cladé, P. & Guellati-Khélifa, S. Determination of the fine-structure constant with an accuracy of 81 parts per trillion. Nature 588, 61–65 (2020).

    Article  ADS  Google Scholar 

  28. Mount, B. J., Redshaw, M. & Myers, E. G. Atomic masses of 6Li, 23Na, 39,41K, 85,87Rb, and 133Cs. Phys. Rev. A 82, 042513 (2010).

    Article  ADS  Google Scholar 

  29. Parker, R. H., Yu, C., Zhong, W., Estey, B. & Müller, H. Measurement of the fine-structure constant as a test of the Standard Model. Science 360, 191–195 (2018).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Sponar, S., Sedmik, R. I. P., Pitschmann, M., Abele, H. & Hasegawa, Y. Tests of fundamental quantum mechanics and dark interactions with low-energy neutrons. Nat. Rev. Phys. 3, 309–327 (2021).

    Article  Google Scholar 

  31. Hori, M. et al. Buffer-gas cooling of antiprotonic helium to 1.5 to 1.7 K, and antiproton-to–electron mass ratio. Science 354, 610–614 (2016).

    Article  ADS  Google Scholar 

  32. Borchert, M. J. et al. A 16-parts-per-trillion measurement of the antiproton-to-proton charge-mass ratio. Nature 601, 53–57 (2022).

    Article  ADS  Google Scholar 

  33. Delaunay, C. et al. Self-consistent extraction of spectroscopic bounds on light new physics. Phys. Rev. Lett. 130, 121801 (2023).

    Article  ADS  Google Scholar 

  34. Patra, S. et al. Proton-electron mass ratio from laser spectroscopy of HD+ at the part-per-trillion level. Science 369, 1238–1241 (2020).

    Article  ADS  Google Scholar 

  35. Biesheuvel, J. et al. Probing QED and fundamental constants through laser spectroscopy of vibrational transitions in HD+. Nat. Commun. 7, 10385 (2016).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  37. Bressel, U. et al. Manipulation of individual hyperfine states in cold trapped molecular ions and application to HD+ frequency metrology. Phys. Rev. Lett. 108, 183003 (2012).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  39. Hollik, W. G., Linster, M. & Tabet, M. A study of New Physics searches with tritium and similar molecules. Eur. Phys. J. C 780, 661 (2020).

    Article  ADS  Google Scholar 

  40. Alighanbari, S., Hansen, M. G., Korobov, V. I. & Schiller, S. Rotational spectroscopy of cold and trapped molecular ions in the Lamb–Dicke regime. Nat. Phys. 14, 555 (2018).

    Article  Google Scholar 

  41. Schneider, T., Roth, B., Duncker, H., Ernsting, I. & Schiller, S. All-optical preparation of molecular ions in the rovibrational ground state. Nat. Phys. 6, 275–278 (2010).

    Article  Google Scholar 

  42. Bakalov, D., Korobov, V. & Schiller, S. Magnetic field effects in the transitions of the HD+ molecular ion and precision spectroscopy. J. Phys. B: At. Mol. Opt. Phys. 44, 025003 (2011).

    Article  ADS  Google Scholar 

  43. Schiller, S., Bakalov, D., Bekbaev, A. K. & Korobov, V. I. Static and dynamic polarizability and the Stark and blackbody-radiation frequency shifts of the molecular hydrogen ions \({{{{\rm{H}}}}}_{2}^{+}\), HD+, and \({{{{\rm{D}}}}}_{2}^{+}\). Phys. Rev. A 89, 052521 (2014).

    Article  ADS  Google Scholar 

  44. Karr, J.-P., Hilico, L., Koelemeij, J. C. J. & Korobov, V. I. Hydrogen molecular ions for improved determination of fundamental constants. Phys. Rev. A 94, 050501 (2016).

    Article  ADS  Google Scholar 

  45. Bakalov, D., Korobov, V. I. & Schiller, S. High-precision calculation of the hyperfine structure of the HD+ ion. Phys. Rev. Lett. 97, 243001 (2006).

    Article  ADS  Google Scholar 

  46. Haidar, M. Hyperfine Structure in the Hydrogen Molecular Ions. PhD thesis, Univ. Sorbonne (2021).

  47. Schiller, S. & Korobov, V. Test of time-dependence of the electron and nuclear masses with ultracold molecules. Phys. Rev. A 71, 032505 (2005).

    Article  ADS  Google Scholar 

  48. Tiesinga, E., Mohr, P. J., Newell, D. B. & Taylor, B. N. Values of Fundamental Physical Constants https://physics.nist.gov/cuu/Constants/index.html (2019).

  49. Korobov, V. I. & Zhong, Z.-X.Bethe logarithm for the \({{{{{\rm{H}}}}}_{2}}^{+}\) and HD+ molecular ions. Phys. Rev. A 86, 044501 (2012).

    Article  ADS  Google Scholar 

  50. Kloor, H., Fischbach, E., Talmadge, C. & Greene, G. L. Limits on new forces coexisting with electromagnetism. Phys. Rev. D 49, 2098–2113 (1994).

    Article  ADS  Google Scholar 

  51. Karshenboim, S. G. Precision physics of simple atoms and constraints on a light boson with ultraweak coupling. Phys. Rev. Lett. 104, 220406 (2010).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We are indebted to C.-J. Kwong and V. A. Vogt for contributing to the reference laser characterization, to E. Wiens for assistance with the frequency comb measurements and to M. G. Hansen for the maser characterization. The studies of additional rovibrational transitions were performed with crucial contributions by M. R. Schenkel. We thank V. I. Korobov for providing the BSM force sensitivities and the spin-averaged frequency value, as well as for helpful comments on the paper. We thank him and J.-Ph. Karr for the communication of results on the hyperfine structure before publication. O. Kullie provided some theoretical data. We are indebted to J. Leute and P. Uhrich for their gracious help with the maser stability characterization. We thank G. Morigi for a helpful discussion. We appreciate the important suggestions of the reviewers. This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 786306, ‘PREMOL’ (S.S.)) and from both Deutsche Forschungsgemeinschaft (DFG) and the state of Nordrhein-Westfalen via grants INST-208/737-1 FUGG (S.S.), INST-208/774-1 FUGG (S.S.) and INST-208/796-1 FUGG (S.S.).

Author information

Authors and Affiliations

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

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

Authors
  1. S. Alighanbari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. V. Kortunov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. S. Giri
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. Schiller
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

S.A. and I.V.K. contributed equally to this work. S.A., I.V.K. and G.S.G. performed the experiments and analysed the data. I.V.K. developed and characterized the laser system. S.A. maintained the apparatus. S.S. performed the analyses and wrote the paper. All authors contributed to review of the data and paper contents.

Corresponding author

Correspondence to S. Schiller.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks Piotr Wcislo and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Spectral characteristics of the 1.15 μm spectroscopy laser.

Left: (red) spectrum analyzer trace of the heterodyne beat of the reference laser 1 (1.06 μ m) and an independent sub-Hz-linewidth, low-drift frequency-stable laser of nearly same optical frequency (reference laser 2, 1.06 μ m); (inset, blue) the heterodyne beat between the spectroscopy laser and the spectrally closest mode of the frequency comb, while the spectroscopy laser is phase-locked to the comb and the comb is phase-locked to the reference laser 1. The solid lines are the lorentzian fits to the data points. The frequency offsets are arbitrary. The linewidths of the two beats and additional characterizations indicate that the spectroscopy laser has a linewidth of less than 10 Hz. Resolution bandwidth of the spectrum analyzer: 1 Hz, red trace - single sweep, sweep time 6 s, blue trace - average of 10 sweeps, time span of 1 min. The error bars are smaller than data markers. Right: (blue) Allan deviation of the frequency of the spectroscopy laser, measured relative to a hydrogen maser (maser 1) via the frequency comb; (green) Allan deviation of maser 1 relative to a second independent maser (maser 2). The shown values are the Allan deviation of the beat frequency divided by \(\sqrt{2}\); (red) Allan deviation of the beat of the reference laser 1 with reference laser 2. The error bars are estimated as 68% confidence intervals.

Extended Data Fig. 2 Sensitivity of transitions and their ratios to BSM forces.

The sensitivity is defined as X−1(dX/dβ), where \(X={f}_{{v}^{{\prime} }}\) or \({{{{\mathcal{R}}}}}_{a,b}\), and is computed as described in Methods, Sec. 1.5. β has units of energy. (a): case of a BSM force between proton and deuteron, proportional to βpd. (b): case of a BSM force between electron and proton, proportional to βep. Full lines denote positive values, dashed lines negative values. The brown, cyan, and gray lines in panel (b) are very close.

Extended Data Fig. 3 Comparison of results on the fundamental mass ratio μ/me.

μ = mpmd/(mp + md) is the reduced proton-deuteron mass. “Penning traps” (dark cyan): computed using the CODATA 2018 value for me/u (that relies mostly on ref. 21), md/u23, md/mp24. CODATA 2018 (black): μ/me computed using only the CODATA values for me/u, mp/u, md/u. The vertical line corresponds to zero of x axis. Note that the value and uncertainty of the “CODATA 2018” entry is significantly correlated with the “Penning traps” entry. LSA-1 is based on f1 (cyan) and f5 (brown); LSA-1b is based on f0 (green), f1 (cyan) and f5 (brown). LSA-1b and LSA-3 (ED Table 5) are nearly identical. As can be seen, the results of the least-squares adjustments deviate from the respective weighted means of the included frequencies. This is due to the assumption of near-perfect correlation rQED of the theoretical uncertainties. The error bars represent standard uncertainty.

Extended Data Fig. 4 Hyperfine structure energy levels of HD+ in the two relevant rovibrational levels.

Shown are the values \({E}_{{{{\rm{spin}}}},p}^{({{{\rm{theor}}}})}/h\) for the ground vibrational level (v = 0, N = 0) (left) and \({E}_{{{{\rm{spin}}}},q}^{({{{\rm{theor}}}})}/h\) for the excited vibrational level \(({v}^{{\prime} }=5,{N}^{{\prime} }=1)\) (right) of the \({}^{2}{\Sigma }_{g}^{+}\) ground electronic state. The vertical axis is broken for better visualization. The numbers next to the arrows indicate the line numbers i(p, q), where p (q) denotes the particular lower (upper) spin state. In this work, line 12 and line 21 were measured. G1 refers to the sum of electron and proton spin, G2 to the sum of G1 and deuteron spin, and F to the sum of G2 and rotational angular momentum N. The ground rovibrational level has zero rotational angular momentum, N = 0, giving rise to 4 spin states with total angular momentum F = 0, 1, 2. The upper rovibrational level \(({v}^{{\prime} }=5,\,{N}^{{\prime} }=1)\) has 10 spin states, having values \({F}^{{\prime} }=0,\,1,\,2,\,3\). For both studied lines 12 and 21, the lower and upper hyperfine states have the same particle spin coupling \({G}_{1}={G}_{1}^{{\prime} }\) and \({G}_{2}={G}_{2}^{{\prime} }\). The line 12 measured here is analogous to line 12 in ref. 3 and to line 12 in ref. 4. The line 21 is analogous to line 16 in ref. 3. Spin states with total angular momentum F are (2F + 1)-fold degenerate in zero magnetic field. We denote the lines and corresponding transition frequencies in zero external fields by fline i. i indicates the position in the list {fspin,i} of the spin frequency values of all spin components in ascending order.

Extended Data Table 1 Spin hamiltonian coefficients, spin structure frequencies, and spin frequency derivatives
Full size table
Extended Data Table 2 Contributions to the ab initio spin averaged frequency f5(theor)
Full size table
Extended Data Table 3 Properties of transitions that have been measured and calculated with high precision
Full size table
Extended Data Table 4 Ratios \({{{\mathcal{R}}}}\) of spin-averaged transition frequencies
Full size table
Extended Data Table 5 Least-squares adjustment LSA-3
Full size table

Supplementary information

Supplementary Information

Supplementary Sections A and B, Fig. 1 and Table 1.

Source data

Source Data Fig. 2

Coordinates of each data point and their uncertainties.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alighanbari, S., Kortunov, I.V., Giri, G.S. et al. Test of charged baryon interaction with high-resolution vibrational spectroscopy of molecular hydrogen ions. Nat. Phys. 19, 1263–1269 (2023). https://doi.org/10.1038/s41567-023-02088-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-023-02088-2

Search

Advanced search

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