Measurement of the bound-electron g-factor difference in coupled ions.

Quantum electrodynamics (QED) is one of the most fundamental theories of physics and has been shown to be in excellent agreement with experimental results1-5. In particular, measurements of the electron's magnetic moment (or g factor) of highly charged ions in Penning traps provide a stringent probe for QED, which allows testing of the standard model in the strongest electromagnetic fields6. When studying the differences between isotopes, many common QED contributions cancel owing to the identical electron configuration, making it possible to resolve the intricate effects stemming from the nuclear differences. Experimentally, however, this quickly becomes limited, particularly by the precision of the ion masses or the magnetic field stability7. Here we report on a measurement technique that overcomes these limitations by co-trapping two highly charged ions and measuring the difference in their g factors directly. We apply a dual Ramsey-type measurement scheme with the ions locked on a common magnetron orbit8, separated by only a few hundred micrometres, to coherently extract the spin precession frequency difference. We have measured the isotopic shift of the bound-electron g factor of the isotopes 20Ne9+ and 22Ne9+ to 0.56-parts-per-trillion (5.6 × 10-13) precision relative to their g factors, an improvement of about two orders of magnitude compared with state-of-the-art techniques7. This resolves the QED contribution to the nuclear recoil, accurately validates the corresponding theory and offers an alternative approach to set constraints on new physics.