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Journal of Physics B Atomic Molecular and Optical Physics

Radio frequency field-induced persistent long-range ordered structures in two-species ion Coulomb crystals

A Mortensen, E Nielsen, Thierry Matthey, Michael Drewsen

Published Jul 25, 2007• 13 citations
Publisher

Abstract

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 quadrupole-trapping field. The results have implications for such diverse research fields as cold molecular ion studies and quantum information processing.

DOI
10.1088/0953-4075/40/15/f01

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Acta Physica Sinica•Sep 29, 2022•1 citation
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 quadrupole-trapping field. The results have implications for such diverse research fields as cold molecular ion studies and quantum information processing.
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.
In this contribution, we present results on the structural properties of single‐component as well as two‐component ion Coulomb crystals confined in a linear Paul trap. Metastable long range ordered structures as the face‐centered cubic (fcc) and body‐centered cubic (bcc) lattices are observed in single‐component ion crystals of sizes down to ∼ 1000 ions. In the case of two‐component ion crystals we observe a stable long range ordered structure in one of the trapped components, which is compared with a Molecular Dynamics (MD) simulation of a two‐component crystal.
Linear strings of trapped atomic ions held in radio-frequency (rf) traps constitute one of the leading platforms for quantum simulation experiments, allowing the investigation of interacting quantum matter.However, linear ion strings have drawbacks, such as the difficulty of scaling beyond approximately 50 particles as well as the inability to naturally implement spin models with more than one spatial dimension.Here we present experiments with planar Coulomb crystals of up to 105 40 Ca + ions in a novel monolithic rf trap, laying the groundwork for quantum simulations of two-dimensional spin models with singleparticle control.We characterize the trapping potential by analysis of crystal images and compare the observed crystal configurations with numerical simulations.We further demonstrate stable confinement of large crystals, free of structural configuration changes, and find that rf heating of the crystal is not an obstacle for future quantum simulation experiments.Finally, we prepare the out-of-plane motional modes of planar crystals consisting of up to 105 ions close to their ground state by electromagnetically induced transparency cooling, an important prerequisite for implementing long-range entangling interactions.
We have carried out a molecular-dynamics simulation of hundreds of ions confined in a Paul trap. The simulation includes the trapped particles' micromotion and interparticle Coulomb interactions. We have implemented a random walk in velocity to bring the secular motion to a given temperature which we have numerically measured. When the coupling \ensuremath{\Gamma} is large the ions form concentric shells which undergo a quadrupole oscillation at the rf frequency, while the ions within a shell form a 2D hexagonal lattice. Ion clouds at 5 mK show no rf heating for qz{\mathit{q}}_{\mathit{z}}qz​\ensuremath{\lesssim}0.6, whereas rapid heating is seen for qz{\mathit{q}}_{\mathit{z}}qz​=0.8.
We report on structural properties of two-component Coulomb crystals in a linear Paul trap. The crystals consist of two laser cooled ion species, 24Mg+ and 40Ca+. The lighter 24Mg+ ions form an inner cylindrical crystal structure surprisingly similar to that of an infinitely long single component crystal, while the outermost shell of the surrounding 40Ca+ ions have a spheroidal shape, which is highly insensitive to the presence of the 24Mg+ ions. Observed changes in the radial separation of the two ion species with the radius of the inner cylindrical crystal is explained by a simple model.
Coulomb crystals have applications in many areas such as quantum computing and simulation, quantum logic spectroscopy, nonlinear dynamics and chaos, phase transitions, and chemical reaction process. The structure of the Coulomb crystal and the trajectory of each trapped ion are typically determined by the parameters of the trap and the ion species. However, dark ions are often inevitable in experiment, which introduces uncertainty into the desired crystal structures and ion trajectories. Few researches have been conducted to investigate the configuration change of the crystal in the presence of dark ions and the influence of a dark ion on its surrounding ion trajectories in a multi-ion system. In this work, we utilize the molecular dynamics simulation software LAMMPS and the (py)LIon package (modified to adapt the semi-classical theory of laser cooling) for simulating the three-dimensional ion trajectories of Coulomb crystals. The formation process of 40Ca+ Coulomb crystal in a linear trap is simulated. With the micromotion and secular motion trajectories of each ion, we calculate the temperature of Coulomb crystal and the average velocity of specific ions. It is observed that the crystal structure exhibits obvious layering phenomenon when the trapped ions yield a large difference in their charge-to-mass ratio (CMR), however, layering is not obvious with a small difference in the CMR. In addition, we simulate and compare the Coulomb crystal structure formed by pure 40Ca+ ions with that formed by 40Ca+ ions mixed with a small number of dark ions including isotopic ions (44Ca+) and impurity ions (CaH+). Three different cases are investigated, namely the one-dimensional ion string, two-dimensional planar structure and three-dimensional helical structure. The results show that the ions in the neighborhood of a dark ion exhibit around micron-order position change compared with their positions before the dark ion is formed. Such a change can be measured in experiment through microscopic imaging, thereby providing a way to identify the formation of dark ions in Column crystals with a large ion number.