Development of an experiment for trapping, cooling, and spectroscopy of molecular hydrogen ions

Abstract

An experiment aimed at high-resolution spectroscopy of the rotational vibrational levelstructure of cold hydrogen molecular ions, HD$^+$, is presented.The molecular hydrogen ion, HD$^+$, as one of the simplest molecules, is outstandinglysuitable for theoretical calculations which shall be compared to experimental data. Itallows direct spectroscopic tests of quantum-electrodynamics and relativistic correctionsin molecules. Furthermore, once theory and experiment both achieve an accuracy betterthan $2cdot 10^{-9}$ the spectroscopic values of the ro-vibrational transitionfrequencies of HD$^+$ can be used to obtain a more accurate value of the fundamentalconstant $m_e / m_p$. In addition if a very high stability of the HD$^+$ transitionfrequencies can be achieved, improved tests of the time invariance of $m_e / m_p$ couldbe performed.The HD$^+$ molecular ions will be confined in a linear rf Paul trap and sympatheticallycooled by interaction with laser cooled Be$^+$ stored in the same trap. The linear rfPaul trap has the main advantage not to require any magnetic field, which could be aproblem for high resolution spectroscopy. A linear trap is used instead of a classicalhyperbolic shaped, because this configuration provides more trapped molecular ions in thefree-field region at less second order Doppler shift.The molecules are cooled sympathetically by Beryllium ions. The laser cooling light at $313;$nm is produced in a new setup of doubly resonantsum-frequency generation (DR-SFG) in LBO. UV radiation of $> 2,$mWoutput power around $313,$nm is generated. A coarse tuning range of 6,nm, a continuoustunability of $> 15$,GHz (which is required for fast and efficient cooling of theinitially hot ions), a sub-MHz linewidth, a frequency drift below 20,MHz/h, and stablelong-term operation is obtained. The theory of optimized doubly-resonant SFG is alsogiven.