Quasiequilibrium Characterization of Mixed-Ion Coulomb Crystals

We demonstrate the application of reliable methods to determine both the average micromotion energies and the number of sympathetically cooled ions (SCIs) embedded in mixed-ion Coulomb crystals in a linear Paul trap. The number of the SCIs and the micromotion energies for the observed mixed-ion crystals are determined by comparing experimentally obtained images with molecular-dynamics simulations, where the kinetic energies of SCIs trapped in rf fields are averaged in cold elastic collisions between the laser-cooled ions and virtual very light atoms. This combined method quickly achieves the quasiequilibrium state of large mixed Coulomb crystals with over 10(3) ions, regardless of the initial conditions, and shows that the previously used pseudopotential-based adiabatic approximations should be replaced by such molecular-dynamics simulations. In addition, a pattern-matching recognition procedure is introduced which objectively ascertains the number of ions. We also apply the presented characterization method to determine the reaction-rate constant between slow acetonitrile molecules and sympathetically cooled Ne+ ions at a translational temperature lower than 10 K.