With the reliably operating Electron Beam Ion Trap (EBIT) at the Max Planck Institute for Nuclear Physics (MPIK) and the projected highly charged ion trap facility at GSI Helmholtzzentrum für Schwerionenforschung (GSI), our collaboration possesses unique experimental equipment to investigate and test some of the most fundamental properties of quantum nature. Highly charged ions offer extremely strong forces and are well-controlled in traps. This usually allows studying small effects due to the quantum nature of the environmental vacuum with high precision. In this way, we plan to measure the g-factor of strongly bound electrons as well as (anti)protons and to pursue a high-precision test of quantum electrodynamics (QED). Furthermore, non-perturbative QED will be tested for highly charged few-electron ions, where previous EBIT-measurements on forbidden transitions already exceed the precision of competing experiments by more than two orders of magnitude. In the near future, experiments will exploit the European XFEL facility and make use of the ultra-cold cryogenic storage ring at MPIK. They will be complemented by non-perturbative theoretical investigations both without and with the presence of laser fields. Examples include the study of radiative corrections to the decay of metastable ionic states and many-body QED effects in the relaxation of heavy ions.
