Fundamental physics with molecular hydrogen ions*

Molecular hydrogen ions (MHI) are three-body quantum systems composed of two simple nuclei and one electron. Compared to the hydrogen atom family, MHIs provide new opportunities for fundamental physics because their internal energy depends not only on the electron-nucleus but also on the nucleus-nucleus interaction and on the nuclear masses. The relative simplicity of MHIs allows successful predictions by ab initio theory, that as of today has reached a precision approaching that of the hydrogen atom theory.

We have performed precise rotational and vibrational spectroscopy of trapped HD⁺, sympathetically cooled by laser-cooled beryllium ions.

Our measurements allow (i) a test of the correctness of the high-precision theory results, (ii) a determination of certain fundamental constants, and (iii) testing for hypothetical deviations of the proton-deuteron interaction from the Coulomb force.

Obtaining precise experimental transition frequencies require a Doppler-free spectroscopy technique. We achieved this with ensembles of molecules rather than with single molecules by loading a moderate number into the linear r.f. trap, where the ions arrange in a string-like fashion on the trap axis. Irradiation of the spectroscopy laser is performed orthogonally to the trap axis. Under these conditions we observed one-photon electric-dipole transitions with resolved carrier, both with THz radiation and with mid-infrared radiation. Line resolution as high as 3×10¹¹ and transition frequency uncertainties as low as 3×10^-12 were achieved.

Measured rotational and vibrational frequencies are in agreement with predictions. Assuming the correctness of the predictions, we determined values of the ratio of reduced nuclear mass and electron mass as well as of the electron-proton mass ratio. Their uncertainties are competitive with the best direct determinations using Penning trap mass spectroscopy. The upper limit for deviations from the nuclear Coulomb force was lowered by more than one order. Opportunities for further progress will be presented.