Three-dimensional long-range ordered structures in smaller and near-spherically symmetric Coulomb crystals of 40 Ca + ions confined in a linear rf Paul trap have been observed when the number of ions exceeds ∼1000 ions. This result is unexpected from ground state molecular dynamics (MD) simulations, but found to be in agreement with MD simulations of metastable ion configurations. Previously, three-dimensional long-range ordered structures have only been reported in Penning traps in systems of ∼50,000 ions or more. [3,4,5,6,7,8,9,10,11] and most recently dusty plasmas [12]. In nature, Coulomb crystals are presently expected to exist in exotic dense astrophysical objects [13].Theoretically, it has been found that the thermodynamic properties of infinite OCPs of a single species, are fully characterized by the coupling parameter [14]where Q is the charge of the particles, a ws is the Wigner Seitz radius defined from the zero temperature particle density n 0 by 4πa 3 ws /3 = 1/n 0 . Furthermore, a liquidsolid transition to a body centered cubic (bcc) structure is expected to occur for Γ ∼ 170 [15,16]. For finite OCPs simulations have shown that the situation is more complex, and the properties will depend both on the size and shape of the ion plasma, since surface effects cannot be neglected [17,18,19,20,21].Ion Coulomb crystals, which for more than a decade have been realized with laser-cooled ion plasmas confined by electromagnetic fields in Penning traps [4,5,9] or in radio-frequency (rf) traps [3,6,7,8,10], offer an excellent opportunity to study finite size effects of OCPs under various conditions. The Coulomb crystal structures studied range from one-dimensional (1D) long cylindrical crystals [3,6,7,8] over 2D thin planar crystals [4] to 3D spheroidal crystals [4,5,6,9]. The 3D spheroidal ion Coulomb crystals reported in Refs. [6,7] are composed of concentric ion shells formed under the influence of the surface of the Coulomb crystals. Simulations indicate that the ions form a near-2D hexagonal short-range ordered structure within each shell [18]. Similarly, shell and short-range order have recently been observed in dusty plasma experiments [12].Observations of three-dimensional long-range order in Coulomb crystals have previously only been reported in the case of ∼50,000 or more laser-cooled ions in a Penning trap [4,5,9]. In contrast to Penning traps, in rf traps Coulomb crystals undergo strong quadrupole deformations at the frequency of the applied rf field due to the so-called micro-motion [22] of the ions. Since this motion is known to produce heating [22,23], it has not been obvious that three-dimensional long-range order could be obtained in such traps.In this Letter, we present observations of long-range structure in Coulomb crystals of 40 Ca + ions confined in a linear rf Paul trap. By varying the number of ions in near-spherically symmetric crystals, we have shown that bcc structures indeed can be observed in such traps even with the number of ions being below a thousand.The linear Paul trap used i...

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Structures of cold bicomponent Coulomb systems of particles with identical charge-to-mass ratios and common oscillation frequency in a spherical harmonic potential are studied by molecular dynamics simulations with up to 10(6) particles. For most initial conditions and cooling rates, the final state becomes a completely mixed core surrounded by a set of nearly degenerated double shells of separate species. For an equal amount of the two species, it is found that the ground state for larger systems consists of a simple cubic structured core surrounded by outer double-shell structures.

We report on the observations of strikingly persistent (lifetimes of ∼10 s) three-dimensional long-range ordered structures in the central 40 Ca + ion component of 40 Ca +-44 Ca + two-species ion Coulomb crystals in a linear Paul trap. Molecular dynamics simulations strongly indicate that the observed structures are a hitherto unpredicted consequence of an effective anisotropy in the inter-particle interaction induced by the radio frequency quadrupoletrapping field. The results have implications for such diverse research fields as cold molecular ion studies and quantum information processing.