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Physical Review A

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

Taro Hasegawa, Tadao Shimizu

Published Dec 12, 2002• 10 citations
Publisher

Abstract

Sympathetic cooling of ${\mathrm{Ca}}^{+},$ ${\mathrm{Zn}}^{+},$ ${\mathrm{Sr}}^{+},$ ${\mathrm{Ba}}^{+},$ and ${\mathrm{Yb}}^{+}$ as guest ions with laser-cooled ${}^{24}{\mathrm{Mg}}^{+}$ 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.

DOI
10.1103/physreva.66.063404

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Sympathetic cooling of Ca+,{\mathrm{Ca}}^{+},Ca+, Zn+,{\mathrm{Zn}}^{+},Zn+, Sr+,{\mathrm{Sr}}^{+},Sr+, Ba+,{\mathrm{Ba}}^{+},Ba+, and Yb+{\mathrm{Yb}}^{+}Yb+ as guest ions with laser-cooled 24Mg+{}^{24}{\mathrm{Mg}}^{+}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.
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{\mathrm{C}}_{60}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.
Abstract Sympathetic cooling is an important technique for achieving low motional temperatures in trapped ion systems that cannot be directly laser cooled. In this paper, we report on the sympathetic cooling of large samples (5 × 10 4 ) of Ba + ions which have been optically pumped into a dark state, using laser cooled Ba + ions in a linear radiofrequency (RF) ion trap. The trap lifetime was evaluated with different dark ion fractions as a function of the RF amplitude, the DC trapping potentials, the power and frequency of the cooling lasers, the quality of the vacuum, and the total number of ions. We found that the RF amplitude was the dominant factor contributing to the loss of ions, and that under optimal conditions and with a dark ion fraction as high as 85%, no losses were observed over 100 s long measurement periods, and fewer than 10% of the ions were lost after 1000 s.
The barium ions are trapped with the laser-cooled magnesium ions simultaneously in an rf trap and cooled sympathetically. Sympathetically cooled ions are one of the candidates of accurate optical frequency standard. The barium ions are ionized by the charge transfer with the magnesium ions for avoiding the loss due to the shallow trapping potential. The temperature of the barium ions is measured and the effect of the sympathetic cooling is observed. It is also found that the application of the ionization by the charge transfer to other ion species is possible.