Resonant oscillation modes of sympathetically cooled ions in a radio-frequency trap

Sympathetic cooling of Ca⁺, Zn⁺, Sr⁺, Ba⁺, and Yb⁺ as guest ions with laser-cooled ²⁴Mg⁺ as host ions in a rf ion trap is carried out, and resonant frequencies of their motion in the trap potential are measured. Various oscillation modes of the sympathetically cooled ions are observed. The resonant frequency of the oscillation mode is different from the frequency of either the collective oscillation frequency of the trapped ions or the oscillation frequency of each ion without host ions. This difference is well explained by a theoretical model in which coupled equations of motion of the host ion cloud with a single guest ion are considered.