Large Ion Crystals in a Linear Paul Trap

Abstract

Plasmas of Mg 1 ions, containing more than 10 5 ions, have been observed to reach well-ordered (crystalline) states by applying laser cooling. The crystals are highly elongated with up to ten concentric cylindrical shells surrounding a central string. Such large structures have not previously been observed in a Paul trap. The amplitude of the micromotion of the ions can be larger than the shell spacings. As the diameter changes along the crystals, sharp transitions are observed when new shells form, in good agreement with molecular dynamics simulations. The predictions from simulations of how ordering develops with decreasing temperature are also confirmed. [S0031-9007(98)07188-9] PACS numbers: 32.80. Pj, 42.50.Vk, 52.25.Wz Clouds of laser-cooled, trapped ions have previously been observed to condense and to exhibit quasicrystalline spatial order in Penning [1,2] and Paul (radiofrequency or rf) traps [3][4][5]. A classical, infinite, one-component plasma undergoes a transition from liquidlike behavior to a body-centered-cubic (bcc) lattice when the ratio G of the Coulomb energy between adjacent particles to the random thermal kinetic energy exceeds 175 [6]. In contrast, for finite plasmas molecular dynamics (MD) simulations predict formation of concentric shells with near-hexagonal ordering within the shell [7,8]. (Though these structures have no long-range periodic order, they are often referred to as crystals, a usage we follow here.)In Paul traps the rf field drives micromotion, which is a modulation (at the rf frequency) of the secular harmonic motion in the effective trapping potential. The magnitude of the micromotion increases with an ion's distance from the trap central axis, and such motion can couple energy from the rf drive into the random motion of the ions through their mutual Coulomb interaction. This so-called rf heating (see, e.g., [9,10]) is widely assumed to limit attainable crystal sizes. The kinetic energy associated with the micromotion can be several orders of magnitude higher than the thermal energy at which spatial ordering occurs in static potentials, so the coupling of micromotion into thermal motion can be expected to be critical for crystal formation. The noninertial constraints and the continually changing shape of the cloud in the rf field can affect the ordering process and the resultant structure of the crystals in interesting ways that at present are poorly understood.Crystals consisting of at most five shells have been attained earlier [5] in a ring rf trap, and simulations with up to 512 ions in a standard Paul trap, with the emphasis on the averaged position of ions in the crystal [11] have been reported previously. By contrast, the largest ordered systems so far were seen in Penning traps, where more than 10 5 ions have been crystallized and show evidence of central bcc structures [2].In this Letter, we present evidence for Coulomb crystals of the largest transverse size observed in a linear Paul trap [12], as well as evidence on how the ordering develops gradually as the r...

Optimization of segmented linear Paul traps and transport of stored particles

“…The Aarhus hexapole design with endcaps [37] and the Innsbruck blade design [38] show a traditional macroscopic approach of mmsize linear trap design without segmentation of the control electrodes. The Michigan trap designs, the microstructured three-layer trap [39] and the semiconductor two-layer trap [40], represent the progress in the miniaturization of linear ion traps and the segmentation of the control electrodes for the transport of single ions and the splitting of ion crystals.…”

Rapid crystallization of externally produced ions in a Penning trap

“…The geometric properties of ion plasmas and the formation of ion Coulomb crystals have been described in detail, for example, in [7,8,[20][21][22][23][24]46,[49][50][51][52]. For the present ion numbers of the order of 1 × 10 3 to 1 × 10 5 ("mesoscopic"), and aspect ratios (axial extension to radial extension) of typically α 1, the so-called planar-shell model is a good approximation to describe the geometry of the confined plasmas.…”

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.…”

“…For simplicity, we neglect any rf modulated motion and ion rotation associated with rf [20] and Penning [15] trapping, respectively. F C n represents the Coulomb forces on ion n from all other ions in the ensemble.…”