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arXiv:0911.3335 · Physical Review A

Crystallization of ion clouds in octupole traps: Structural transitions, core melting, and scaling laws

F. Calvo, C. Champenois, Ersin Yurtsever

Published Dec 1, 2009• 18 citations
arXivHTMLPDF

Abstract

The stable structures and melting properties of ion clouds in isotropic octupole traps are investigated using a combination of semianalytical and numerical models, with a particular emphasis at finite-size scaling effects. Small-size clouds are found to be hollow and arranged in shells corresponding approximately to the solutions of the Thomson problem. The shell structure is lost in clusters containing more than a few thousands of ions, the inner parts of the cloud becoming soft and amorphous. While melting is triggered in the core shells, the melting temperature follows the rule expected for three-dimensional dense particles, with a depression scaling linearly with the inverse radius.

DOI
10.1103/physreva.80.063401

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The stable structures and melting properties of ion clouds in isotropic octupole traps are investigated using a combination of semianalytical and numerical models, with a particular emphasis at finite-size scaling effects. Small-size clouds are found to be hollow and arranged in shells corresponding approximately to the solutions of the Thomson problem. The shell structure is lost in clusters containing more than a few thousands of ions, the inner parts of the cloud becoming soft and amorphous. While melting is triggered in the core shells, the melting temperature follows the rule expected for three-dimensional dense particles, with a depression scaling linearly with the inverse radius.
The stable structures and melting dynamics of clusters of identical ions bound by linear octupole radiofrequency traps are theoretically investigated by global optimization methods and molecular dynamics simulations. By varying the cluster sizes in the range of 10--1000 ions and the extent of trap anisotropy by more than one order of magnitude, we find a broad variety of stable structures based on multiple rings at small sizes evolving into tubular geometries at large sizes. The binding energy of these clusters is well represented by two contributions arising from isotropic linear and octupolar traps. The structures generally exhibit strong size effects, and chiral arrangements spontaneously emerge in many crystals. Sufficiently large clusters form nested, coaxial tubes with different thermal stabilities. As in isotropic octupolar clusters, the inner tubes melt at temperatures that are lower than the overall melting point.
We investigate the structural properties and melting behaviors of two-dimensional ion crystals in an RF trap, focusing on the effects of ion temperature and trap potential symmetry. We identify distinct crystal structures that form under varying trapping conditions and temperatures through experimental observations and theoretical analyses. As the temperature increases or the trap potential becomes more symmetric, we observe a transition from a lattice arrangement to elongated ring-like formations aligned along the trap axes. Our experimental and theoretical efforts enhance our understanding of phase transitions in low-dimensional, confined systems, offering insights into the controlled formation of quantum crystals for applications in quantum simulations and many-body physics.
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.
Fundamental theories and models of many-body physics can be probed in experiments on ultracold atoms held in place by electromagnetic fields. In particular, of considerable interest are systems under curved confinement, since they can yield exotic states of matter which would be impossible to obtain in flat space. In this study we focus on relatively small samples, where curvature effects are stronger, and analyze by Monte Carlo simulations the peculiar structure arising in an assembly of soft-core bosons subject to a trapping potential with spherical symmetry. Upon suitable tuning of the parameters, 100 particles or so group together in clusters arranged in a shell with icosahedral symmetry. As the number of particles increases, a second shell gradually develops, concentric to (and partly overlapping with) the original one, where clusters are in perfect registry with the first shell, thus forming a dodecahedral pattern. Cluster arrangements with the symmetry of other polyhedra are seen for different sets of parameters. At low temperature the superfluid density is nonuniform in the radial direction; heating the system progressively, superfluidity eventually vanishes while still clusters are present, a behavior resembling the transition from supersolid to normal solid on a plane. Two shells of clusters are also observed in systems of classical or distinguishable quantum particles, but in those cases the shells are more fragile to thermal fluctuations.
Planar quadrupole ion traps have been analyzed through numerical and analytic solutions of Laplace's equation. These involve either one or more conducting rings or their analogs, a hole in one or more conducting sheets. The leading terms in the potential are harmonic, corresponding to the Paul trap, but with coefficients that reduce their efficiency and for some traps, the anharmonic terms can be suppressed to eighth-order. Stable ion trapping is predicted for all electrode configurations possessing radial and axial symmetry. A three-hole microtrap with an inner hole radius of 80 \ensuremath{\mu}m trapped from one to many (dense clouds) laser-cooled Ba+{\mathrm{Ba}}^{+}Ba+ ions where the two-ion distance is compressed to 1 \ensuremath{\mu}m, allowing new experiments in quantum optics. Also, arrays of traps for optical clocks are contemplated using photolithographic fabrication.
Confinement of ion clouds in an rf octupole ion trap is investigated with particular emphasis on the trapping stability, which is position dependent. Excitation spectra of trapped clouds of Ba+{\mathrm{Ba}}^{+}Ba+ ions are observed, and the kinetic energy of ion clouds is derived. The spatial extension of ion clouds is measured, providing the basis for an experimental study of the trapping stability. For ion clouds in an rf octupole trap the mean kinetic energy is smaller and the spatial extension is larger than in comparable Paul traps.