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 lattices^2,3 or individual ions in radio-frequency traps^4,5. 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 measurements^10,11. 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 transitions^8,12 in HCIs, which are required for precision studies of fundamental physics⁶.