Precision spectroscopy of molecular hydrogen ions: fundamental constants and BSM physics
Prof. Stephan Schiller (Heinrich-Heine-Universität Düsseldorf, Institut für Experimentalphysik)

Molecular hydrogen ions (MHI), the simplest molecules, are three-body quantum systems composed of two simple nuclei and one electron. They are of high interest for fundamental physics and metrology because they provide the missing link between the fields of mass and g-factor measurements with Penning traps and spectroscopy of hydrogen-like atoms.

Basically, the new ingredients introduced by the MHI are the long-range nucleus-nucleus interaction, absent in the hydrogen atom, and the quantized motion of the nuclei.

Precision spectroscopy of the MHI can thus furnish novel results: (1) on the masses of proton and deuteron (in the future, also of tritium), (2) set limits for beyond-Standard-Model (BSM) forces, (3) verify the wave character of matter, and (4) test alternative theories of quantum mechanics. This is performed by comparing or matching experimental and theoretical rotational and/or vibrational frequencies. The comparison is enhanced by the availability of several recently measured transition frequencies and recent advances in ab initio theory.

An additional opportunity for probing the interactions between the particles within the MHI is the precision measurement of its hyperfine structure (HFS). Only the synthesis of the HFS of the hydrogen atom, of the deuterium atom and of the molecular hydrogen ion allows probing the physics of HFS
at the finest level, resolving the issue of the uncalculable nuclear contributions.

We present recent results of our spectroscopy of sympathetically cooled MHI, its results and interpretation. An outlook on near-future studies is also given.