Laser spectroscopy of highly charged bismuth ions: The hyperfine-puzzle of strong-field QED

Laser spectroscopy of the ground state hyperfine splittings in hydrogen-like and lithium-like bismuth ions (²⁰⁹Bi⁸²⁺ and (²⁰⁹Bi⁸⁰⁺)) tests the theory of bound-state quantum electrodynamics (QED) in the strong field of the nucleus. Precise theoretical predictions use a specific difference of both splitting energies to cancel the large uncertainty of nuclear contributions. The transition in Li-like Bismuth was observed for the first time in 2011, yet the accuracy of the result was limited by the calibration of the electron cooler voltage, determining the ion velocity. Here, we report on improved laser spectroscopic measurements of both hyperfine splittings. The accuracy was improved by about an order of magnitude compared to the first observation in 2011. The most important new feature was an in-situ high voltage measurement system with an accuracy at the 10-ppm level provided by German metrology institute Physikalisch-Technische Bundesanstalt. The experimentally determined specific difference deviates more than 7σ from theory. This so-called hyperfine puzzle might be explained either by unknown effects in the specific difference or by a incorrect value of the nuclear magnetic moment of ²⁰⁹Bi. Recent and future investigations to resolve this puzzle are presented.