Proton–electron mass ratio by high-resolution optical spectroscopy of ion ensembles in the resolved-carrier regime

Optical spectroscopy in the gas phase is a key tool for elucidating the structure of atoms and molecules and their interaction with external fields. The line resolution is usually limited by a combination of first-order Doppler broadening due to particle thermal motion and a short transit time through the excitation beam. For trapped particles, suitable laser cooling techniques can lead to strong confinement (the Lamb–Dicke regime) and thus to optical spectroscopy free of these effects. For non-laser-coolable spectroscopy ions, this has so far only been achieved when trapping one or two atomic ions, together with a single laser-coolable atomic ion 1 , 2 . Here we show that one-photon optical spectroscopy free of Doppler and transit broadening can also be obtained with more easily prepared ensembles of ions, if performed with mid-infrared radiation. We demonstrate the method on molecular ions. We trap ~100 molecular hydrogen ions (HD + ) within a Coulomb cluster of a few thousand laser-cooled atomic ions and perform laser spectroscopy of the fundamental vibrational transition. Transition frequencies were determined with a lowest uncertainty of 3.3 × 10 −12 fractionally. As an application, we determine the proton–electron mass ratio by matching a precise ab initio calculation with the measured vibrational frequency.