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Journal of Physics B Atomic Molecular and Optical Physics

Crystalline ion structures in a Paul trap

M. Block, A. Drakoudis, H Leuthner, P Seibert, Guenter Werth, M. Block, A. Drakoudis, H Leuthner, P Seibert

Published May 16, 2000• 52 citations
Publisher

Abstract

We have observed crystalline structures formed by laser cooled Ca + ions in a three-dimensional confining potential. The potential has been realized using a linear Paul trap with different ratios of potential strength in the axial and radial directions. For radial confining potentials stronger than the axial potential, we find linear structures with a continuous transition from strings to helices with decreasing potential asymmetry. When a quasi-two-dimensional potential is formed we observe ring structures with a given maximum ion number per ring which we followed up to 19. The observations are essentially in agreement with molecular dynamics calculations in static two-dimensional potentials.

DOI
10.1088/0953-4075/33/11/101

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We have observed crystalline structures formed by laser cooled Ca + ions in a three-dimensional confining potential. The potential has been realized using a linear Paul trap with different ratios of potential strength in the axial and radial directions. For radial confining potentials stronger than the axial potential, we find linear structures with a continuous transition from strings to helices with decreasing potential asymmetry. When a quasi-two-dimensional potential is formed we observe ring structures with a given maximum ion number per ring which we followed up to 19. The observations are essentially in agreement with molecular dynamics calculations in static two-dimensional potentials.
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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.
We report on the observations of three-dimensional long-range ordered structures in the central 40^{40}40Ca+^++ ion component of 40^{40}40Ca+^++--44^{44}44Ca+^++ two-species ion Coulomb crystals in a linear Paul trap. In contrast to long-range ordering previously observed in single species crystals, the structures observed are strikingly persistent and always of one specific type in one particular orientation. Molecular dynamics simulations strongly indicate that these characteristics are a hitherto unpredicted consequence of the co-axial cylindrical symmetry of the central ion component of the Coulomb crystal and the radio frequency quadrupole trapping field.
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.
We observed phase transitions and ordered structures of laser-cooled Mg+{\mathrm{Mg}}^{+}Mg+ ions stored in a radio-frequency quadrupole storage ring with a diameter of 115 mm. The ions are confined two dimensionally by a quadrupole field and can move freely along the ring circumference. By cooling the ions with tangentially intersecting laser beams, we observed a linear string of ions aligned along the center line of the quadrupole field. For higher ion densities the linear structure changes into a helical structure. The dynamics of the stored ions was studied.
We have fabricated a miniature three-segment linear Paul trap with r 0=0.6 mm and 2Z 0=4 mm. In order to perform quantum-state manipulation of trapped 40 Ca+ ions, we discuss the required harmonic oscillation frequencies which allow us to perform effective sideband cooling and have measured those that depend on the dimensions of the trap. A laser beam that has a component in the radial direction of the linear trap as well as that propagating along the trap axis has been used to detect the fluorescence spectra of the 42 S 1/2–42 P 1/2 transition. We have observed that the profile of the fluorescence spectrum obtained with the side laser beam is markedly different from that obtained with the axial laser beam due to micromotion. By applying additional DC voltages, the micromotion has been compensated, its amplitude has been estimated, and crystallization has been observed for two 40 Ca+ and four 40 Ca+ ions.