Secular Motion Frequencies of ⁹Be⁺ Ions and ⁴⁰Ca⁺ Ions in Bi-component Coulomb Crystals

We obtain bi-component Coulomb crystals using laser-cooled ⁴⁰Ca⁺ ions to sympathetically cool ⁹Be⁺ ions in a linear Paul trap. The shell structures of the bi-component Coulomb crystals are investigated. The secular motion frequencies of the two different ions are determined and compared with those in the single-component Coulomb crystals. In the radial direction, the resonant motion frequencies of the two ionic species shift toward each other due to the strong motion coupling in the ion trap. In the axial direction, the motion frequency of the laser-cooled ⁴⁰Ca⁺ is impervious to the sympathetically cooled ⁹Be⁺ ions because the spatially separation of the two different ionic species leads to the weak motion coupling in the axial direction. (paper)