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Rotational spectroscopy of cold and trapped molecular ions in the Lamb–Dicke regime

Nature Physics volume 14, pages 555–559 (2018)Cite this article

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Abstract

Sympathetic cooling of trapped ions has been established as a powerful technique for the manipulation of non-laser-coolable ions1,2,3,4. For molecular ions, it promises vastly enhanced spectroscopic resolution and accuracy. However, this potential remains untapped so far, with the best resolution achieved being not better than 5 × 10−8 fractionally, due to residual Doppler broadening being present in ion clusters even at the lowest achievable translational temperatures5. Here we introduce a general and accessible approach that enables Doppler-free rotational spectroscopy. It makes use of the strong radial spatial confinement of molecular ions when trapped and crystallized in a linear quadrupole trap, providing the Lamb–Dicke regime for rotational transitions. We achieve a linewidth of 1 × 10−9 fractionally and 1.3 kHz absolute, an improvement of ≃50-fold over the previous highest resolution in rotational spectroscopy. As an application, we demonstrate the most precise test of ab initio molecular theory and the most accurate (1.3 × 10−9) determination of the proton mass using molecular spectroscopy. The results represent the long overdue extension of Doppler-free microwave spectroscopy of laser-cooled atomic ion clusters6 to higher spectroscopy frequencies and to molecules. This approach enables a wide range of high-accuracy measurements on molecules, both on rotational and, as we project, vibrational transitions.

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Fig. 1: Principle of the Lamb–Dicke rotational spectroscopy of sympathetically cooled molecular ions.
Fig. 2: Characteristics and consequences of the motion of molecular ions in laser-cooled Be+/HD+ Coulomb clusters at different temperatures.
Fig. 3: Simplified diagram of relevant energy levels of HD+ in the ground vibrational level ν = 0 of the \({}^{2}{{\rm{\Sigma }}}_{g}^{+}\) electronic state.
Fig. 4: Spectroscopy of one hyperfine component of the fundamental rotational transition of HD+.

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Acknowledgements

This work has been partially funded by Deutsche Forschungsgemeinschaft project Schi 431/19-1. V.I.K. acknowledges support from the Russian Foundation for Basic Research under grant no. 15-02-01906-a. We thank U. Rosowski for important assistance with the frequency comb, A. Nevsky for assistance with a laser system, E. Wiens for characterizing H-maser instability, D. Iwaschko, R. Gusek and P. Dutkiewicz for electronics development, J. Scheuer and M. Melzer for assistance, and S. Schlemmer (Universität zu Köln) for equipment loans. We thank K. Brown (Georgia Institute of Technology) for useful discussions and suggestions.

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Authors and Affiliations

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

    S. Alighanbari, M. G. Hansen & S. Schiller

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

    V. I. Korobov

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  1. S. Alighanbari
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Contributions

S.A. and M.G.H. developed the apparatus and performed the experiments; S.A., M.G.H. and S.S. analysed the data; S.A., S.S. and V.I.K. performed theoretical calculations; S.S. conceived the study, supervised the work and wrote the paper.

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Correspondence to S. Schiller.

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Alighanbari, S., Hansen, M.G., Korobov, V.I. et al. Rotational spectroscopy of cold and trapped molecular ions in the Lamb–Dicke regime. Nature Phys 14, 555–559 (2018). https://doi.org/10.1038/s41567-018-0074-3

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