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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Manipulating the structure of ion coulomb crystals with light

Péter Horák, Aurélien Dantan, Michael Drewsen

Published May 1, 2011• 0 citations
Publisher

Abstract

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.

DOI
10.1109/cleoe.2011.5943294

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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.
We investigate numerically the structural dynamics of ion Coulomb crystals confined in a three-dimensional harmonic trap when influenced by an additional one-dimensional optically induced periodical potential. We demonstrate that transitions between thermally excited crystal structures, such as body-centered cubic and face-centered cubic, can be suppressed by a proper choice of the potential depth and periodicity. Furthermore, by varying the harmonic trap parameters and/or the optical potential in time, controlled transitions between crystal structures can be obtained with close to unit efficiency.
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.
Light-induced control of ions within small Coulomb crystals is investigated. By intense intracavity optical standing-wave fields, subwavelength localization of individual ions is achieved for one-, two-, and three-dimensional crystals. Based on these findings, we illustrate numerically how the application of such optical potentials can be used to tailor the normal-mode spectra and patterns of multidimensional Coulomb crystals. The results represent, among others, important steps towards controlling the crystalline structure of Coulomb crystals, investigating heat-transfer processes at the quantum limit, and quantum simulations of many-body systems.
We demonstrate light-induced localization of Coulomb-interacting particles in multi-dimensional structures. Subwavelength localization of ions within small multi-dimensional Coulomb crystals by an intracavity optical standing wave field is evidenced by measuring the difference in scattering inside symmetrically red- and blue-detuned optical lattices and is observed even for ions undergoing substantial radial micromotion. These results are promising steps towards the structural control of ion Coulomb crystals by optical fields as well as for complex many-body simulations with ion crystals or for the investigation of heat transfer at the nanoscale, and have potential applications for ion-based cavity quantum electrodynamics, cavity optomechanics and ultracold ion chemistry.
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.
Laser-cooled atomic ions form ordered structures in radiofrequency ion traps and in Penning traps. Here we demonstrate in a Penning trap the creation and manipulation of a wide variety of ion Coulomb crystals formed from small numbers of ions. The configuration can be changed from a linear string, through intermediate geometries, to a planar structure. The transition from a linear string to a zigzag geometry is observed for the first time in a Penning trap. The conformations of the crystals are set by the applied trap potential and the laser parameters, and agree with simulations. These simulations indicate that the rotation frequency of a small crystal is mainly determined by the laser parameters, independent of the number of ions and the axial confinement strength. This system has potential applications for quantum simulation, quantum information processing and tests of fundamental physics models from quantum field theory to cosmology.