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IEEE Transactions on Instrumentation and Measurement

Dynamic properties of ions stored and laser-cooled in a linear trap

M. Tachikawa, Masatoshi Kajita, Toshihiko Shimizu

Published Apr 1, 1993• 4 citations
Publisher

Abstract

The dynamics of ions confined and laser-cooled in an RF/DC hybrid linear trap are studied. Numerical analysis reveals that RF heating due to ion-ion collisions is restricted, and laser-cooled ions are crystallized more effectively in the linear trap than in the conventional hyperboloid RF trap. A simple analytical method is presented to estimate the maximum number of ions which form an ion crystal.>

DOI
10.1109/19.278567

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The dynamics of ions confined and laser-cooled in an RF/DC hybrid linear trap are studied. Numerical analysis reveals that RF heating due to ion-ion collisions is restricted, and laser-cooled ions are crystallized more effectively in the linear trap than in the conventional hyperboloid RF trap. A simple analytical method is presented to estimate the maximum number of ions which form an ion crystal.>
A laser-cooling experiment with Ca+{\mathrm{Ca}}^{+}Ca+ ions trapped in a linear rf octupole ion trap is presented. The phase transition of the laser-cooled Ca+{\mathrm{Ca}}^{+}Ca+ ions from the cloud to the crystal state is observed by an abrupt dip of the laser-induced fluorescence spectrum and indicates that mK temperatures are obtained. We have also performed molecular dynamics simulations under various conditions to confirm this property by deducing axially symmetric structures of Coulomb crystals and by evaluating the translational temperatures of the laser-cooled ions. The simulation results show that for small numbers of ions novel ring-shaped crystals are produced. As the number of ions is increased, cylindrical layers in the ring crystal are sequentially formed. For more than 100 ions, also hexagonal and spiral structures emerge in parts of the large-size ion crystal, which has a length on the order of millimeters for the present geometrical arrangement and voltages. An advantage of the linear rf octupole trap is its large almost-field-free region in the middle of the trap, where the micromotion amplitude is small for trapped ions. These results demonstrate that such a multipole trap has attractive features for quantum computing and ultracold ion-atom collision studies.
A detailed investigation of ion crystals produced by laser and sympathetic cooling in a linear RF trap has been conducted.\n\nThe laser cooling methods were examined and applied to the trapped ^24Mg^(positive) ions. The crystals produced by the laser cooling were studied, including the dependence on RF voltage, end cap DC voltage, laser power and laser frequency. By manipulating the different RF voltages and endcap DC voltages, the structure phase transition of the ion crystals was observed.\n\nIn addition, the sympathetic cooling of different ion species with the laser cooled 24Mg^(positive) was carried out. In this process, the mixed Mg^(positive) and He^(positive) crystals were created andidentified, and mixed Mg^(positive) and H2^(positive) crystals were produced. The effect of an unwanted chemical reaction of Mg^(positive) and H2 was observed and minimized. After sympathetic cooling of light ion species, the sympathetic cooling of heavy molecular ions such as fullerene ions was also carried out. The efficiencies and final temperature in both cases are very different. Theoretically to interpret the results, molecular dynamics simulations of the laser cooling and sympathetic cooling were implemented. And the simulations were compared with the experimental results.\n\nIn the process of carrying out this research, the optics were rebuilt to provide reliable UV sources for the photoionization and laser cooling of Mg ions. The imaging\nsystem was reconfigured to take the images of ion crystals. New elements were added tin the ion trap to improve the ability to manipulate ions.
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.
Trapped singly charged ions can crystallize as a result of laser cooling. The emerging structure depends on the number of particles and on the geometry of the trapping potential. In linear multipole radio frequency traps, the geometry of the radial potential can lead to the formation of single-ring structures. We analyze the conditions and stability of single rings as a function of the number of poles. The rings form tubes for a large number of ions and sufficiently small trap aspect ratios. In these structures the arrangement of the ions corresponds to a triangular lattice folded onto a cylinder. The stability of the tubular structures is numerically studied for different lattice constants and their normal-mode spectrum is determined.
Molecular dynamics simulations of the ion clouds stored in a linear quadrupole rf ion trap are performed at low temperatures (0.1 mK--15 K). The introduction of periodic boundary conditions allowed us to study the translationally uniform ion cloud geometry. The time evolution of the kinetic energy of the ion cloud is monitored during the simulation and the increase in the kinetic energy of the cloud (rf heating) is determined; its dependence on temperature, trapping voltage, and the number of ions is studied. The dependence of rf heating rate on temperature shows that rf heating is undetectable until the temperature reaches approximately 0.5 K; it then increases rapidly until it reaches a maximum at around 2 K. It starts to decrease slowly at higher temperatures. The rf heating rate is shown to increase very sharply with the amplitude of the trapping voltage. The dependence of the rf heating rate on the number of ions shows the influence of the ion crystal shell structure at low temperatures, and has a simple linear dependence at higher temperatures.