Sympathetic cooling of a mass-mismatched two-ion chain in a double-well trap potential

Sympathetic cooling of two-ion system, in which one is laser-cooled and the other is sympathetically cooled and their masses are mismatched, in a linear rf trap with a double-well potential is proposed. The double-well potential consists of two wells, and there is one ion in each well. The axial frequencies of the two wells and the spatial interval between them are experimentally controllable. By theoretical analysis, the normal modes of the small oscillations around the equilibrium are derived, and a measure of the sympathetic cooling rate is obtained. As a result, it is found that the sympathetic cooling rate is fast when the frequency of the axial motion of the sympathetically cooled ion is close to that of the laser-cooled ion. In the double-well potential, the sympathetic cooling rate of the ion species whose mass is much heavier or lighter than that of the laser-cooled ion can be fast. The sympathetic cooling rate of C₆₀⁺ by the laser-cooled Ba⁺ in the double-well potential is estimated to be about 80 times faster than in the conventional setup. The double-well potential may be made by the microfabricated electrode configuration or by the optical dipole force trap.