Structure and Madelung energy of spherical Coulomb crystals

Abstract

With the help of molecular-dynamics computer simulations, we study the equilibrium con6gurations of systems of N =2 -5000 strongly correlated charged particles under the influence of a radial harmonic external confining force and their mutual Coulomb forces. The temperature is well below the crystallization point; i.e. , the ratio of Coulomb to kinetic energy is as large as 1 = 10 . The particles arrange in concentric spherical shells with approximately constant intershell distances. On the surfaces plane hexagonal structures are well pronounced. The calculated radii, occupation numbers, and energies per particle are compared with results of classical geometrical and shell models with homogeneously charged shells corrected for hexagonal surface occupation. The closed-shell particle numbers also agree well with those of multilayer icosahedra. From the computer simulations we extract a Madelung (excess) energy of -0.8926, which is close to the theoretical value of the shell model corrected for plane hexagonal surfaces, -0.8923, but larger than the one of the infinite geometrical lattice, -0.8944, and of the bcc value of -0.8959. Surface-energy eÃects are positive and of the order of N PACS number(s): 32.80. Pj, 52.25.b, 52.65.+z, 52.75.Di

Crystallization of ion clouds in octupole traps: Structural transitions, core melting, and scaling laws

“…This shell structure can be fruitfully used to predict the minima for larger clouds, assuming that the radial density is written as a sum over M concentric shells of zero thickness. Such a shell model was initially developed for the quadrupole trap [27] and improved for intra-shell correlations [28]. The energy to be minimized, Φ shell , is a function of the radii {R i } of the shells, each shell i carrying N i ions (plus one possible ion at the center, N 0 ):…”

Finite-temperature crossover from a crystalline to a cluster phase for a confined finite chain of ions

“…An early study of the structure of spherical Coulomb crystals [18] showed that particles are arranged in concentric spherical shells with constant intershell distances and a hexagonal surface structure. Furthermore, for large systems a bcc lattice is formed in the interior [19] resembling the case of infinite Coulomb systems (One Component Plasma) [20].…”

Optically induced structural phase transitions in ion Coulomb crystals

“…Ty, 37.10.Vz, 64.70.kp, 36.40.Ei When an ensemble of confined ions with the same sign of charge is cooled to a sufficiently low temperature, the ionic system forms a crystalline structure [1], often referred to as an ion Coulomb crystal. Since the first experimental realizations of ion Coulomb crystals through laser cooling of atomic ions into the milli-Kelvin regime in electromagnetic traps [2,3], there has been growing theoretical [4][5][6][7][8][9][10][11][12][13][14] and experimental [15][16][17][18][19][20][21][22][23][24] interest in studying the structural and dynamic properties of these crystals under different trapping conditions and for various ion compositions.The unique localization and isolation of the individual ions constituting the crystals have already led to a large number of amazing results within precision measurements [25], cavity quantum electrodynamics (CQED) [26][27][28][29][30], quantum information science [31][32][33][34][35], and cold molecular science [36][37][38][39]. For experiments involving larger three-dimensional ion Coulomb crystals, such as CQED related experiments [26,27] with the interesting prospect of creating quantum memories and other quantum devices, ...…”

“…Ty, 37.10.Vz, 64.70.kp, 36.40.Ei When an ensemble of confined ions with the same sign of charge is cooled to a sufficiently low temperature, the ionic system forms a crystalline structure [1], often referred to as an ion Coulomb crystal. Since the first experimental realizations of ion Coulomb crystals through laser cooling of atomic ions into the milli-Kelvin regime in electromagnetic traps [2,3], there has been growing theoretical [4][5][6][7][8][9][10][11][12][13][14] and experimental [15][16][17][18][19][20][21][22][23][24] interest in studying the structural and dynamic properties of these crystals under different trapping conditions and for various ion compositions.…”

“…While the energetic ground state of very large threedimensional Coulomb crystals ( > ∼ 10 5 ions) in a harmonic confinement is known to be a body-centered cubic (bcc) lattice [1], the energetically most favorable configuration for smaller crystals ( < ∼ 10 3 ions) is ions situated in concentric shells [5]. For medium sized crystals often employed in experiments [26, 27] (∼ 10 3 − 10 5 ions), the structure is generally not very stable, and thermally induced transitions between a large variety of states including metastable bcc and fcc structures and incommensurable crystallite formations can be observed [40,41].…”