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

TL;DR

This paper demonstrates high-resolution optical spectroscopy of molecular ion ensembles in the resolved-carrier regime, enabling precise measurement of fundamental constants like the proton-electron mass ratio.

Contribution

It introduces a method to perform Doppler-free spectroscopy on ion ensembles using mid-infrared radiation, extending techniques previously limited to single or few ions.

Findings

Achieved Doppler-free spectroscopy on about 100 molecular ions.

Measured vibrational transition frequencies with an uncertainty of 3.3×10^{-12}.

Determined the proton-electron mass ratio by comparing experimental results with ab initio calculations.

Abstract

Optical spectroscopy in the gas phase is a key tool to elucidate the structure of atoms and molecules and of 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 of a short transit time through the excitation beam. For trapped particles, suitable laser cooling techniques can lead to strong confinement (Lamb-Dicke regime, LDR) 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 approximately 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 lowest uncertainty of 3.3$\times$10$^{-12}$ fractionally. As an application, we determine the proton-electron mass ratio by matching a precise ab initio calculation with the measured vibrational frequency.