Laser-Cooled Ion Crystals

Birkl, G.; Kassner, S.; Walther, H.

doi:10.1051/epn/19922308143

Cited by 16 publications

(9 citation statements)

References 8 publications

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“…In the absence of additional smaller particles, the ground state of such a system corresponds to a (1,6,11,20) configuration, as shown by numerical simulations. 21 Obviously, the presence of the 10 smaller particles leads only to a slight modification of the ground state compared to the monodisperse system.…”

Section: Resultsmentioning

confidence: 75%

Binary colloidal systems in two-dimensional circular cavities: Structure and dynamics

Mangold

Birk

Leiderer

et al. 2004

Phys. Chem. Chem. Phys.

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We study the melting behavior of a binary system (R ¼ 4.5 mm, r ¼ 2.8 mm) of paramagnetic colloidal spheres in two-dimensional (2D) circular cavities. A repulsive interaction between the particles is caused by an external magnetic field B that induces magnetic dipole moments perpendicular to the sample plane. By means of video microscopy, we investigate the positions of the particles and their trajectories. For small interaction strengths, we observe a completely liquid phase where large and small particles diffuse across the entire system. With increasing B the larger particles become-due to their larger magnetic moment-localized and form a stable structure while the smaller particles behave still as a liquid. For even higher magnetic fields, the small particles also become increasingly localized and preferentially arrange as interstitial sites between the structures formed by the large particles. We present a systematic study of this rather complex multi-stage melting process which strongly depends on the particle numbers of large and small particles.

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Section: Resultsmentioning

confidence: 75%

Binary colloidal systems in two-dimensional circular cavities: Structure and dynamics

Mangold

Birk

Leiderer

et al. 2004

Phys. Chem. Chem. Phys.

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“…However, while the KTHNY theory applies only for extended 2D systems, much less (both experimentally and theoretically) is known about the properties of 2D systems which are only comprised of a few particles (typically less than N = 100). Due to the finitness of such systems a different melting scenario compared to infinite systems is expected which may be important for the understanding of melting and freezing of, e.g., small 2D clusters or ions in radiofrequency traps [6]. It has been experimentally demonstrated that when super paramagnetic colloidal particles are confined to a circular hard-wall cavity, the particles at low effective temperatures T eff do not crystallize in a triangular lattice, but are rather arranged in a shell-like structure with both positional and orientational order.…”

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Fluctuation-induced order in two-dimensional colloidal clusters

Bubeck¹,

Leiderer²,

Bechinger³

2002

Europhys. Lett.

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PACS. 82.70.Dd -Colloids. PACS. 64.60.Cn -Order-disorder transformations; statistical mechanics of model systems. PACS. 83.10.Tv -Structural and phase changes.Abstract. -The behavior of a finite number (N = 29) of paramagnetic colloidal particles in 2D circular hard-wall cavities is investigated. By applying a magnetic field B, the interaction between the particles is varied. We demonstrate that the angular diffusion of the particles which are arranged in shells is highly anisotropic and shows a non-monotonic behavior as a function of B. When reducing radial particle fluctuations in one shell by a ring-shaped optical tweezer, the relative angular diffusion between adjacent shells increases again. This clearly demonstrates that radial particle fluctuations are responsible for an enhanced registration between adjacent shells.Thermal fluctuations are well known to have a strong influence on the phase behavior of two-dimensional (2D) systems compared to their three-dimensional counterparts [1]. The most striking evidence for such a difference is probably the melting transition which is, in 2D, predicted to occur via two sequential defect-driven continuous phase transitions as described by the KTHNY theory (see, e.g., [2]). Amongst conveniently accessible experimental systems for basic investigations of 2D melting colloidal particles have been established as model systems because they allow direct optical observation of topological defects and comparison to theoretical predictions [3][4][5]. However, while the KTHNY theory applies only for extended 2D systems, much less (both experimentally and theoretically) is known about the properties of 2D systems which are only comprised of a few particles (typically less than N = 100). Due to the finitness of such systems a different melting scenario compared to infinite systems is expected which may be important for the understanding of melting and freezing of, e.g., small 2D clusters or ions in radiofrequency traps [6]. It has been experimentally demonstrated that when super paramagnetic colloidal particles are confined to a circular hard-wall cavity, the particles at low effective temperatures T eff do not crystallize in a triangular lattice, but are rather arranged in a shell-like structure with both positional and orientational order. Upon increasing the temperature first orientational order between adjacent shells is lost which is typically refered to as intershell rotation. As the temperature is increased further, a "re-entrant" ordered phase is observed which is followed by complete melting of the cluster [7]. While intershell rotation is also observed in numerical studies of finite 2D systems of ions or electrons in circular cavities, the "re-entrant" ordered phase as found in the experiments, is still c EDP Sciences

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“…Dd, 64.60.Cn, 83.20.Hn During the past decade there has been considerable progress in the localization and cooling of ions and electrons in artificial confining fields. Typical examples for three-dimensional (3D) and two-dimensional (2D) systems are ions in radio frequency traps [1], electrons on the surface of liquid He [2,3], and electrons in quantum dots [4], respectively. With the help of present-day powerful imaging techniques such examples may be promising subjects for the experimental investigation of systems in lateral confinements.…”

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confidence: 99%

Melting and Reentrant Freezing of Two-Dimensional Colloidal Crystals in Confined Geometry

et al. 1999

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We study the melting behavior of a finite number (N # 45) of paramagnetic colloidal spheres in a two-dimensional circular hard wall cavity. The interaction strength between the particles is varied by applying a magnetic field B. At high B, i.e., strong interaction, the particles are arranged in a highly ordered shell-like structure. With decreasing B we observe first a loss of angular order between adjacent shells. Upon further reduction of the external B field, however, angular order is restored again before the system melts completely. We propose a simple mechanism to account for this reentrance phenomenon. [S0031-9007(99)08972-3] PACS numbers: 82.70. Dd, 64.60.Cn, 83.20.Hn During the past decade there has been considerable progress in the localization and cooling of ions and electrons in artificial confining fields. Typical examples for three-dimensional (3D) and two-dimensional (2D) systems are ions in radio frequency traps [1], electrons on the surface of liquid He [2,3], and electrons in quantum dots [4], respectively. With the help of present-day powerful imaging techniques such examples may be promising subjects for the experimental investigation of systems in lateral confinements. Additionally the structural and dynamical properties of few-body systems are also attractive from the theoretical point of view. Several authors considered 2D systems with finite numbers of ions or electrons in lateral confinements using Monte Carlo (MC) simulations [5][6][7][8][9]. At low temperatures and in the case of a small number of particles, the clusters are found not to crystallize in a triangular lattice (Wigner crystal), but are arranged in a shell structure. Accordingly, it was pointed out that such systems may be a "realization" of a 2D Thomson atom where the structure as a function of the particle number can be analyzed in terms of a Mendeleev-type table [7]. The melting of laterally confined 2D systems with particle numbers on the order of 100 or smaller is theoretically predicted to occur via a two step process [7][8][9]. Upon increasing the temperature, first intershell rotation becomes possible where orientational order between adjacent shells is lost. At even higher temperatures radial diffusion between shells sets in which finally destroys positional order. This scenario differs considerably from what is generally predicted to occur in infinite 2D systems when the temperature is raised [10][11][12][13].In this paper we present an experimental study of the phase behavior of a 2D system in a circular hard wall confinement. As particles we used superparamagnetic colloidal spheres whose pair potential can be varied over a wide range by an external magnetic field B. The advantages of colloidal suspensions as model systems are their convenient time (milliseconds) and length scales (microns) which allow the detailed observation of single particle trajectories by means of video microscopy [14,15]. At high B, i.e., strongly repulsive forces between the particles, we observe a shell structure displaying radial ...

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Laser-Cooled Ion Crystals

Cited by 16 publications

References 8 publications

Binary colloidal systems in two-dimensional circular cavities: Structure and dynamics

Binary colloidal systems in two-dimensional circular cavities: Structure and dynamics

Fluctuation-induced order in two-dimensional colloidal clusters

Melting and Reentrant Freezing of Two-Dimensional Colloidal Crystals in Confined Geometry

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