Stringent test of QED with hydrogen-like tin.

Inner-shell electrons naturally sense the electric field close to the nucleus, which can reach extreme values beyond 10 15  V cm -1 for the innermost electrons 1 . Especially in few-electron, highly charged ions, the interaction with the electromagnetic fields can be accurately calculated within quantum electrodynamics (QED), rendering these ions good candidates to test the validity of QED in strong fields. Consequently, their Lamb shifts were intensively studied in the past several decades 2,3 . Another approach is the measurement of gyromagnetic factors (g factors) in highly charged ions 4-7 . However, so far, either experimental accuracy or small field strength in low-Z ions 5,6 limited the stringency of these QED tests. Here we report on our high-precision, high-field test of QED in hydrogen-like 118 Sn 49+ . The highly charged ions were produced with the Heidelberg electron beam ion trap (EBIT) 8 and injected into the ALPHATRAP Penning-trap setup 9 , in which the bound-electron g factor was measured with a precision of 0.5 parts per billion (ppb). For comparison, we present state-of-the-art theory calculations, which together test the underlying QED to about 0.012%, yielding a stringent test in the strong-field regime. With this measurement, we challenge the best tests by means of the Lamb shift and, with anticipated advances in the g-factor theory, surpass them by more than an order of magnitude.