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Physical Review A

Optically induced structural phase transitions in ion Coulomb crystals

Péter Horák, Aurélien Dantan, Michael Drewsen

Published Oct 31, 2012• 10 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.86.043435

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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 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.
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.
Abstract We investigate the structural transitions of ion Coulomb crystals (ICCs) using molecular dynamics simulations, focusing on the effects of ion number and the anisotropy of the confining potential. Our simulations reveal transitions from linear to zigzag to shell formation and dissolution to a two-dimensional plane finally. We characterized the phase transition points, the number of phase transitions. This study provides a more detailed analysis than previous works and establishes a power-law relationship between the critical anisotropy parameter and ion number. Our results offer valuable insights for the precise determination of ICC structure, trapped ion counting, and trapping potential parameters in experimental settings.
The electronic and motional degrees of freedom of trapped ions can be controlled and coherently coupled on the level of individual quanta.Assembling complex quantum systems ion by ion while keeping this unique level of control remains a challenging task.For many applications, linear chains of ions in conventional traps are ideally suited to address this problem.However, driven motion due to the magnetic or radio-frequency electric trapping fields sometimes limits the performance in one dimension and severely affects the extension to higher-dimensional systems.Here, we report on the trapping of multiple barium ions in a single-beam optical dipole trap without radio-frequency or additional magnetic fields.We study the persistence of order in ensembles of up to six ions within the optical trap, measure their temperature, and conclude that the ions form a linear chain, commonly called a one-dimensional Coulomb crystal.As a proof-of-concept demonstration, we access the collective motion and perform spectrometry of the normal modes in the optical trap.Our system provides a platform that is free of driven motion and combines advantages of optical trapping, such as state-dependent confinement and nanoscale potentials, with the desirable properties of crystals of trapped ions, such as long-range interactions featuring collective motion.Starting with small numbers of ions, it has been proposed that these properties would allow the experimental study of many-body physics and the onset of structural quantum phase transitions between one-and two-dimensional crystals.
We study experimentally and theoretically structural defects which are formed during the transition from a laser cooled cloud to a Coulomb crystal, consisting of tens of ions in a linear radio frequency trap. We demonstrate the creation of predicted topological defects ("kinks") in purely two-dimensional crystals and also find kinks which show novel dynamical features in a regime of parameters not considered before. The kinks are always observed at the center of the trap, showing a large nonlinear localized excitation, and the probability of their occurrence saturates at ∼0.5. Simulations reveal a strong anharmonicity of the kink's internal mode of vibration, due to the kink's extension into three dimensions. As a consequence, the periodic Peierls-Nabarro potential experienced by a discrete kink becomes a globally confining potential, capable of trapping one cooled defect at the center of the crystal.
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.