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Japanese Journal of Applied Physics

Motional Resonances of Sympathetically Cooled 44Ca+, Zn+, or Ga+ Ions in a Linear Paul Trap

Yoshiki Kai, Kenji Toyoda, Masayoshi Watanabe, Shinji Urabe

Published Aug 1, 2001• 9 citations
Publisher

Abstract

44Ca+, Zn+, or Ga+ ions are sympathetically cooled by Coulomb interaction with laser-cooled 40Ca+ ions, and motional resonances of these ions are observed by monitoring the fluorescence of the 40Ca+ ions. In the experiment of sympathetic cooling of 44Ca+, the ratio of the decrease in the fluorescence signal at the motional resonance of the sympathetically cooled species to that at the motional resonance of the laser-cooled species is almost proportional to the number ratio of the two species. In the case of Ga+ ions as the sympathetically cooled species, the change in the response of sympathetically cooled species becomes larger as the temperature of the ion cloud decreases. Crystallization of an ion cloud which contains both 40Ca+ and Zn+ (or Ga+) is observed.

DOI
10.1143/jjap.40.5136

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44Ca+, Zn+, or Ga+ ions are sympathetically cooled by Coulomb interaction with laser-cooled 40Ca+ ions, and motional resonances of these ions are observed by monitoring the fluorescence of the 40Ca+ ions. In the experiment of sympathetic cooling of 44Ca+, the ratio of the decrease in the fluorescence signal at the motional resonance of the sympathetically cooled species to that at the motional resonance of the laser-cooled species is almost proportional to the number ratio of the two species. In the case of Ga+ ions as the sympathetically cooled species, the change in the response of sympathetically cooled species becomes larger as the temperature of the ion cloud decreases. Crystallization of an ion cloud which contains both 40Ca+ and Zn+ (or Ga+) is observed.
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.
A two-ion pair in a linear Paul trap is extensively used in the research of the simplest quantum-logic system; however, there are few quantitative and comprehensive studies on the motional mode coupling of two-ion systems yet. This study proposes a method to investigate the motional mode coupling of sympathetically cooled two-ion crystals by quantifying three-dimensional (3D) secular spectra of trapped ions using molecular dynamics simulations. The 3D resonance peaks of the 40Ca+–27Al+ pair obtained by using this method were in good agreement with the 3D in- and out-of-phase modes predicted by the mode coupling theory for two ions in equilibrium and the frequency matching errors were lower than 2%. The obtained and predicted amplitudes of these modes were also qualitatively similar. It was observed that the strength of the sympathetic interaction of the 40Ca+–27Al+ pair was primarily determined by its axial in-phase coupling. In addition, the frequencies and amplitudes of the ion pair’s resonance modes (in all dimensions) were sensitive to the relative masses of the ion pair, and a decrease in the mass mismatch enhanced the sympathetic cooling rates. The sympathetic interactions of the 40Ca+–27Al+ pair were slightly weaker than those of the 24Mg+–27Al+ pair, but significantly stronger than those of 9Be+–27Al+. However, the Doppler cooling limit temperature of 40Ca+ is comparable to that of 9Be+ but lower than approximately half of that of 24Mg+. Furthermore, laser cooling systems for 40Ca+ are more reliable than those for 24Mg+ and 9Be+. Therefore, 40Ca+ is probably the best laser-cooled ion for sympathetic cooling and quantum-logic operations of 27Al+ and has particularly more notable comprehensive advantages in the development of high reliability, compact, and transportable 27Al+ optical clocks. This methodology may be extended to multi-ion systems, and it will greatly aid efforts to control the dynamic behaviors of sympathetic cooling as well as the development of low-heating-rate quantum logic clocks.
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.
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.
We study the spatial structure and sympathetic cooling of the bi-component Coulomb crystal (CC), which consists of approximate 450 9Be+ ions and 450 40Ca+ ions with a mass ratio of 0.225 in a segmented linear ion trap. By two-dimensional imaging of the bi-component CC, the 9Be+ ions are found to be surrounded by the 40Ca+ ions in the radial direction with a separation ratio of ∼ 2.0, and the axial length of the 9Be+ ions occupied area is much larger than that of the 40Ca+ ions occupied area. Combined with the previous experimental results, the structure of the 9Be+–40Ca+ CC shows the larger the difference in the mass–charge ratio, the larger the separation between the two species. The comparison of the fluorescence spectra of the 9Be+ ions in the bi-component CC and the pure CC indicates that the 9Be+ ions can be sympathetically cooled and stably localized by the laser-cooled 40Ca+ ions during the recording of the fluorescence spectrum.
We investigated sympathetic Coulomb crystallization of CaH+{}^{+}+ ions produced by a laser-induced reaction through an excited state according to 40Ca^{40}\mathrm{Ca}40Ca+{}^{+}+(4p2P1/24p {}^{2}{P}_{1/2}4p2P1/2​) +++ H2{\mathrm{H}}_{2}H2​ $\ensuremath{\rightarrow}$ 40Ca^{40}\mathrm{Ca}40CaH+{}^{+}+ +++ H. 40Ca^{40}\mathrm{Ca}40CaH+{}^{+}+ ions stored in a linear Paul trap were characterized by their secular-motion excitation spectrum and by the modified fluorescence images of crystallized Ca+{}^{+}+ ions. The number of two-species crystallized ions, the secular motion temperature, and the structure were determined by molecular dynamics simulations. Both the observed two-species ion crystals and simulation images demonstrate that the CaH+{}^{+}+ ions were sympathetically crystallized with their secular-motion temperature being less than 10 mK. We determined reaction rates from fluorescence images of two-species Coulomb crystals by systematically changing the reaction time. In addition a lower limit for the reaction rate coefficient $k=8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ cm3{}^{3}3/s was obtained.