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arXiv:1202.2544

Direct imaging of thermally excited metastable structures of ion Coulomb clusters

Michael Drewsen, Thierry Matthey, A. Mortensen, J. P. Hansen

Published Feb 12, 2012• 2 citations
arXivHTMLPDF

Abstract

Coulomb crystallisation of large ensembles of ions has in the past years been intensively studied experimentally with many spectacular results of relevance to infinite systems in one-, two-, and three-dimensions.While strings of a few ions have proven to be very attractive objects in quantum information processing, larger Coulomb crystals have very recently found applications within other aspects the dynamics of quantum systems. Smaller finite ensembles of cold identical charged particles confined by a harmonic potential furthermore constitute very special types of clusters due to the pure repulsive long-range inter-particle forces. Here, we report on the direct imaging of metastable structures of Coulomb clusters consisting of a few thousands confined and laser-cooled 40Ca+ ions. The observations are attributed to structural excitations due to finite temperatures, a feature likely to appear in clusters of short-range interacting particles, but yet not observed directly.

DOI
10.48550/arxiv.1202.2544

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Coulomb crystallisation of large ensembles of ions has in the past years been intensively studied experimentally with many spectacular results of relevance to infinite systems in one-, two-, and three-dimensions.While strings of a few ions have proven to be very attractive objects in quantum information processing, larger Coulomb crystals have very recently found applications within other aspects the dynamics of quantum systems. Smaller finite ensembles of cold identical charged particles confined by a harmonic potential furthermore constitute very special types of clusters due to the pure repulsive long-range inter-particle forces. Here, we report on the direct imaging of metastable structures of Coulomb clusters consisting of a few thousands confined and laser-cooled 40Ca+ ions. The observations are attributed to structural excitations due to finite temperatures, a feature likely to appear in clusters of short-range interacting particles, but yet not observed directly.
Coulomb crystallisation of laser-cooled ensembles of ions in harmonic traps has been studied experimentally with many spectacular results in recent years. It is well known that for sufficiently large numbers of ions the ground state of a Coulomb crystal in such a system has a body-centred cubic (bcc) structure. However, in experiments with crystals of up to a few 104 ions, structural transitions between bcc and, for example, face centred cubic (fee) or hexagonal close packed (hep) structures are observed. For constant ion densities, the lattice spacing of the planes of highest density differs only by about 3% between bcc and fee structures and simulations predict very small energy differences, thus thermal effects even at temperatures in the mK regime are sufficient to excite these transitions. Here we study numerically the possibility of controlling and switching the crystal structure with the help of periodic potentials generated by the dipole forces of standing-wave light fields.
Ion Coulomb crystals are ordered structures formed by laser-cooled ions in traps that are characterized by interparticle distances of several micrometers and energy scales on the order of μμμeV. Their crystalline structure emerges from the interplay between Coulomb repulsion and the external confining potential, which can be readily tuned. Moreover, individual ions can be precisely manipulated with lasers and imaged via resonance fluorescence. These unusual and unique properties make ion crystals a powerful platform for studying phases of matter in the strongly correlated regime and at low temperatures where their dynamics is manifestly quantum mechanical. This review examines the theoretical framework and experimental characterization of ion Coulomb crystals from a condensed-matter perspective. We discuss their dynamical and thermodynamic properties in one, two, and three dimensions, and review recent investigations into their out-of-equilibrium behavior. We provide outlooks on future directions for exploring novel condensed matter phenomena with trapped ion crystals, as well as for exploiting these features for scientific and technical applications.
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.
Laser cooling of atomic ions has long been used as a tool in physics to explore quantum entanglement for applications in quantum computing and information. More recently, laser-cooled atomic ions have been used as a platform for studying cold chemistry. Here, we describe an experimental system called a “Coulomb crystal,” where laser-cooled ions are confined in traps at sufficiently low translational energies that they form an ordered structure. We then present a range of experiments undertaken using this platform, from studies of reactions with an atomic species to reaction systems of increased complexity, involving molecular ions and neutral molecules. We also describe a few spectroscopic studies enabled by Coulomb crystals before discussing some possible future directions of the field. This is not meant to be a comprehensive review of the entire field, but rather a sampling of the types of experiments that can be performed and the knowledge gained from these studies.
Coulomb crystal yields a wide range of applications including quantum computing and simulation, phase transitions, quantum logic spectroscopy, nonlinear dynamics and chaos, chemical reaction process, etc. 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 experiments, which introduces uncertainty to the desired crystal structures and ion trajectories. Few research has 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 paper, we utilize the molecular dynamics simulation software LAMMPS and the (py)Lion package (modified to adapt the semi-classical theory of laser cooling) for the simulation of the 3D ion trajectories of Coulomb crystals. The formation process of 40Ca+ Coulomb crystals 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’s 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 and 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 1D ion string, 2D plane structure and 3D helical structure. Results show that ions in the neighborhood of a dark ion exhibit around micron-order position changes compared to their positions before the dark ion is formed. Such a change can be measured in experiment through microscopic imaging, providing a way to identify dark ions in Column crystals with a large number of ions.
Abstract We demonstrate that the earlier suggested new all-optical method of creating long-term small (containing two or three particles) ion clusters using the rectified optical forces (RFs) can be used to create cold trapped Coulomb crystals (consisting of several tens of resonant ions). The results of the supercomputer simulations of the dynamics of a mercury ion cloud in a polychromatic optical superlattice (induced by RFs) are presented and analysed. Such a cloud (including 49 ions) in the absence of the optical field expands rapidly (during the characteristic time of the order of ) as a result of the Coulomb explosion. It is shown that the polychromatic optical field can result in the ‘quenching’ of the Coulomb explosion and crystallisation of the ion cloud: creation of a quasi-2D array of ordered and strongly coupled cold ions (with the Coulomb coupling parameter and temperature ∼10 −3 K). The mean destruction time of the studied metastable crystal is of the order of 10 s. Moreover, the central core of the ion cloud can retain its crystalline configuration for a much longer time.