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Physical Review A

Limiting temperature of sympathetically cooled ions in a radio-frequency trap

Taro Hasegawa, Tadao Shimizu

Published Jan 29, 2003• 7 citations
Publisher

Abstract

The limiting temperature achieved by sympathetic cooling in an rf trap is calculated with a theoretical model in which no fitting parameters are used. The calculated result agrees well with observation. The dependence of the temperature on trapping parameters and ion mass is also analyzed. The results can be used for designing an rf trap system.

DOI
10.1103/physreva.67.013408

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IEEE Transactions on Instrumentation and Measurement•Apr 1, 2001•3 citations
The limiting temperature achieved by sympathetic cooling in an rf trap is calculated with a theoretical model in which no fitting parameters are used. The calculated result agrees well with observation. The dependence of the temperature on trapping parameters and ion mass is also analyzed. The results can be used for designing an rf trap system.
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 laser cooling of ions stored within a linear-geometry, radio frequency, electric-quadrupole trap has been investigated using computational and theoretical techniques. The simulation, which allows five sample ions to interact with 35 laser-cooled atomic ions, revealed an instability heating mechanism, which can prevent ions below a certain critical mass from being sympathetically cooled. This critical mass can, however, be varied by changing the trapping field parameters, thus allowing ions with a very large range of masses to be sympathetically cooled using a single ion species. A theoretical explanation of this instability heating mechanism is presented which predicts that the cooling-heating boundary in trapping parameter space is a line of constant qu{q}_{u}qu​ (ion trap stability coefficient), a result supported by the computational results. The threshold value of qu{q}_{u}qu​ depends on the masses of the interacting ions. A functional form of this dependence is given.