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Detection of metastable electronic states by Penning trap mass spectrometry


State-of-the-art optical clocks1 achieve precisions of 10−18 or better using ensembles of atoms in optical lattices2,3 or individual ions in radio-frequency traps4,5. Promising candidates for use in atomic clocks are highly charged ions6 (HCIs) and nuclear transitions7, which are largely insensitive to external perturbations and reach wavelengths beyond the optical range8 that are accessible to frequency combs9. However, insufficiently accurate atomic structure calculations hinder the identification of suitable transitions in HCIs. Here we report the observation of a long-lived metastable electronic state in an HCI by measuring the mass difference between the ground and excited states in rhenium, providing a non-destructive, direct determination of an electronic excitation energy. The result is in agreement with advanced calculations. We use the high-precision Penning trap mass spectrometer PENTATRAP to measure the cyclotron frequency ratio of the ground state to the metastable state of the ion with a precision of 10−11—an improvement by a factor of ten compared with previous measurements10,11. With a lifetime of about 130 days, the potential soft-X-ray frequency reference at 4.96 × 1016 hertz (corresponding to a transition energy of 202 electronvolts) has a linewidth of only 5 × 10−8 hertz and one of the highest electronic quality factors (1024) measured experimentally so far. The low uncertainty of our method will enable searches for further soft-X-ray clock transitions8,12 in HCIs, which are required for precision studies of fundamental physics6.

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Fig. 1: Results of the Re measurements at PENTATRAP.
Fig. 2: The 4d10 ground state and relevant 4d94f excited electronic states of the 187Re29+ ion.

Data availability

The datasets analysed in this study are available from the corresponding author.

Code availability

The experimental data were analysed using OriginLab and a self-written analysis script, which is available from the corresponding author. The Quanty code and its documentation are available from MCDHF 1 is described in ref. 51 and MCDHF 2 in ref. 55.


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This article comprises parts of the PhD thesis work of H.C., to be submitted to Heidelberg University, Germany. This work is supported by the German Research Foundation (DFG) Collaborative Research Centre SFB 1225 (ISOQUANT) and by the DFG Research UNIT FOR 2202. P.I. acknowledges partial support from NIST. Laboratoire Kastler Brossel (LKB) is supported by Unité Mixte de Recherche de Sorbonne Université, de ENS-PSL Research University, du Collége de France et du CNRS No. 8552. P.I., Y.N.N. and K.B. are members of the Allianz Program of the Helmholtz Association, contract number EMMI HA-216 ‘Extremes of Density and Temperature: Cosmic Matter in the Laboratory’. P.I. thanks J.-P. Desclaux for help in improving the MCDFGME code. This project received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement number 832848 - FunI. Furthermore, we acknowledge funding and support by the International Max Planck Research School for Precision Tests of Fundamental Symmetries (IMPRS-PTFS) and by the Max Planck, RIKEN, PTB Center for Time, Constants and Fundamental Symmetries.

Author information




The experiment was performed by R.X.S., M.D., A.R. and S.E. The data were analysed by R.X.S. and S.E. Theoretical calculations were performed by H.B., M.B., H.C., Z.H., M.W.H. and P.I. The manuscript was written by R.X.S., M.B., Z.H., M.W.H., P.I., J.R.C.L.-U. and S.E. and edited by S.U. and K.B. All authors discussed and approved the data as well as the manuscript.

Corresponding authors

Correspondence to R. X. Schüssler or S. Eliseev.

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Peer review information Nature thanks Jens Dilling, Marianna Safronova and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Schüssler, R.X., Bekker, H., Braß, M. et al. Detection of metastable electronic states by Penning trap mass spectrometry. Nature 581, 42–46 (2020).

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