Collisional cooling of internal rotation in MgH$^+$ ions trapped with He atoms: Quantum modeling meets experiments in Coulomb crystals

Abstract: Using the ab initio computed Potential Energy Surface (PES) for the electronic interaction of the MgH$^+$ ($^1\Sigma$) ion with the He($^1$S) atom, we calculate the relevant state-changing rotationally inelastic collision cross sections from a quantum treatment of the multichannel scattering problem. We focus on the quantum dynamics at the translationally low energies for the present partners discussed in the earlier, cold ion trap experiments (see below) which we wish to model in detail. The corresponding state-changing rates computed between the lower rotational states of the molecular ion are employed to describe the time-evolution kinetics followed by recent experiments on Coulomb-crystalized MgH$^+$ ($^1\Sigma$), where the ions are rotationally cooled by micromotion tuning after the uploading into the trap of He as a buffer gas. The present computational modeling of the final ions' rotational temperatures in the experiments turns out to agree very well with their observations and points at a fast equilibration between rotational and thermal temperatures of the ions.