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arXiv:physics/0208069 · Physical Review A

Instability heating of sympathetically cooled ions in a linear Paul trap

T. J. Harmon, N. Moazzan-Ahmadi, R. I. Thompson

Published Jan 31, 2003• 7 citations
arXivHTMLPDF

Abstract

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 ${q}_{u}$ (ion trap stability coefficient), a result supported by the computational results. The threshold value of ${q}_{u}$ depends on the masses of the interacting ions. A functional form of this dependence is given.

DOI
10.1103/physreva.67.013415

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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.
An investigation of the sympathetic cooling \nmethod for the studies of large ultra-cold molecular ions in a quadrupole ion trap has been conducted.Molecular dynamics simulations are performed to study the rf heating mechanisms in the ion trap. The dependence of \nrf heating rates on the ion temperature, trapping parameters, \nand the number of ions is obtained. New rf heating mechanism \naffecting ultra-cold ion clouds exposed to laser radiation is described.The saturation spectroscopy setup of the hyperfine spectra \nof the molecular iodine has been built to provide an accurate frequency reference for the laser wavelength. This reference is used to obtain the fluorescence lineshapes of \nthe laser cooled Mg+^++ ions under different trapping conditions.The ion temperatures are deduced from the measurements, and \nthe influence of the rf heating rates on the fluorescence lineshapes \nis also discussed. Cooling of the heavy (m=720m=720m=720a.u.) fullerene ions to under 10K by the means of the sympathetic cooling by the Mg+^++ ions(m=24m=24m=24a.u.) is demonstrated. The single-photon imaging system has been developed and used to obtain the images of the Mg+^++ ion crystal structures at mK temperatures.
Coulomb crystals, containing up to a few hundred ions of which more than 50% were cooled sympathetically by the Coulomb interaction with laser cooled Mg+ ions, have been produced in a linear Paul trap. By controlling the balance of the radiation pressure from the two cooling lasers, the Coulomb crystals could be segregated according to ion species. Previous studies of ion crystals and molecular dynamics simulations suggest that the temperature may be around 10 mK or lower. The obtained results indicate that a wide range of atomic and molecular ions, which due to their internal structures are not amenable to direct laser cooling, can be effectively cooled and localized (crystallized) in linear Paul traps. For high resolution spectroscopy of such ions this may turn out to be very useful.
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We have created multispecies Coulomb crystals in a linear Paul trap containing up to a few hundred ions of which more than 5050%50 were cooled only sympathetically through the Coulomb interaction with laser-cooled Mg+{\mathrm{Mg}}^{+}Mg+ ions. In an extreme case, one laser-cooled ion maintained order in a 15 ion string. Ion species segregation was obtained by radiation pressure. Previous experiments and molecular dynamics simulations suggest the temperature is 10 mK or lower. These results indicate that a wide range of atomic and molecular ions can be cooled and localized in linear Paul traps which is important for improvements in spectroscopic studies of such ions.
Long-range polarization forces between ions and neutral atoms result in large elastic scattering cross sections (e.g., $\ensuremath{\sim}\phantom{\rule{-0.16em}{0ex}}\phantom{\rule{-0.16em}{0ex}}{10}^{6}\phantom{\rule{0.28em}{0ex}}\mathrm{a}.\mathrm{u}.$ for Na\mathrm{Na}Na-Na+{\mathrm{Na}}^{+}Na+ or Na\mathrm{Na}Na-Ca+{\mathrm{Ca}}^{+}Ca+ at cold and ultracold temperatures). This suggests that a hybrid ion-neutral trap should offer a general means for significant sympathetic cooling of atomic or molecular ions. We present simion 7.0 simulation results concerning the advantages and limitations of sympathetic cooling within a hybrid trap apparatus consisting of a linear rf Paul trap concentric with a Na\mathrm{Na}Na magneto-optical trap (MOT). This paper explores the impact of various heating mechanisms on the hybrid system and how parameters related to the MOT, Paul trap, number of ions, and ion species affect the efficiency of the sympathetic cooling.
We investigate the problem of a single ion in a radio-frequency trap and immersed in an ultracold Bose gas either in condensed or non-condensed phase. We develop master equation formalism describing the sympathetic cooling and we determine the cooling rates and final energies of ions. We show that cold atomic reservoir modifies the stability diagram of the ion in the Paul trap creating the regions where the ion is either cooled or heated due to the energy quanta exchanged with the time-dependent potential. Our calculation indicates that micromotion constitutes an important source of heating limiting the final temperature of ions to values higher than 100μ\muμK for parameters of present experiments.