Structural properties of two-component coulomb crystals in linear paul traps

We report on structural properties of two-component Coulomb crystals in a linear Paul trap. The crystals consist of two laser cooled ion species, 24Mg+ and 40Ca+. The lighter 24Mg+ ions form an inner cylindrical crystal structure surprisingly similar to that of an infinitely long single component crystal, while the outermost shell of the surrounding 40Ca+ ions have a spheroidal shape, which is highly insensitive to the presence of the 24Mg+ ions. Observed changes in the radial separation of the two ion species with the radius of the inner cylindrical crystal is explained by a simple model.     

Secular Motion Frequencies of ~9Be~+ Ions and ~(40)Ca~+ Ions in Bi-component Coulomb Crystals

We obtain bi-component Coulomb crystals using laser-cooled ~(40)Ca~+ ions to sympathetically cool ~9Be~+ ions in a linear Paul trap. The shell structures of the bi-component Coulomb crystals are investigated. The secular motion frequencies of the two different ions are determined and compared with those in the single-component Coulomb crystals. In the radial direction, the resonant motion frequencies of the two ionic species shift toward each other due to the strong motion coupling in the ion trap. In the axial direction, the motion frequency of the laser-cooled~(40)Ca~+is impervious to the sympathetically cooled ~9Be~+ ions because the spatially separation of the two different ionic species leads to the weak motion coupling in the axial direction.     

Theory and simulation of ion Coulomb crystal formation in a Penning trap

Ion Coulomb crystals (ICCs) are formed by laser-cooled ions in both radio-frequency and Penning traps. In radio-frequency traps, the crystals are generally stationary. In Penning traps, ICCs always rotate. The frequency of rotation is often set by an applied rotating wall drive that forces the crystal to rotate at the same frequency as the drive. In the absence of any applied rotating or oscillating fields, ICCs in a Penning trap can be in stable equilibrium with a range of rotation frequencies. The density and shape of the crystal adjust with the rotation frequency to ensure that equilibrium is reached. Here, we show that the parameters of the radial laser-cooling beam determine the rotation frequency of a small crystal in a Penning trap when no driving fields are present. We demonstrate, using an approximate theoretical treatment and realistic simulations, that the crystal rotation frequency is independent of the number of ions and the trap parameters, so long as the crystal radius remains smaller than the cooling laser beam waist. As the rotation frequency increases, the crystal eventually becomes a linear string, at which point it is no longer able to adjust its density. Instead, a small amplitude vibration in the zigzag mode of oscillation manifests itself as a rotation of the crystal at a fixed frequency that depends only on the applied trap potential.     

Structural properties of vapor-grown C60 crystals

Vapor grown crystals of C₆₀ with thin flat triangular, rhombic or trapezoidal shapes of size to 1×2×0.001 mm as well as prismastic crystals typically 0.5×0.4×0.2 mm have been grown using a high temperature vapor transport method. Room temperature X-ray precession photography shows these crystals exhibit diffraction patterns consistent with those for either (a) single or (b) twinned crystals of the previously reported face-centered cubic structure or (c) a more complex cell of hexagonal symmetry with a=10.010(2) Å and c=49.064(11) Å. This latter from actually is a multiple twin containing both the face-centered cubic and the close-packed hexagonal structure types. The sharp diffraction maxima for either the single or the twinned crystals demonstrate that they consist of large coherent domains and are essentially free of planar defects parallel to the twin planes.     

Fission lifetimes of Th nuclei measured by crystal blocking

Crystal blocking lifetime measurements have been made for highly excited Th nuclei with neutron number well removed from the stability line. Thin W crystals were bombarded with ³²S ions in the energy range 170-180 MeV and the yield of fission fragments was measured for emission close to a 〈111〉 axis. The fission blocking dips are compared to the appropriately scaled ones for elastic scattering of the ³²S beam ions and no significant difference is seen between the dips. This implies that the fraction of nuclei fissioning with lifetimes longer than 10 as is less than 2%. Fission lifetimes are increased by viscosity in the nuclear mass flow and comparison with a statistical model calculation indicates that the viscosity parameter, η, must be lower than for Th and U nuclei near β-stability. The effect of the N = 126 magic number is discussed. Received: 2 October 2002 / Accepted: 16 January 2003 / Published online: 29 April 2003     

Anharmonic oscillation of ions trapped in a rf trap with light buffer gas

The effect of a light buffer gas on the anharmonic oscillation of ions trapped in a rf trap is studied. The rf resonance absorption signals showed a change of the signal height and the hysteresis with the sweep direction of the dc voltage or the probing frequency due to the anharmonicity of the pseudopotential well of a rf trap. It was found that the signals changed drastically or even disappeared depending on the pressure of buffer gas, although almost the same number of ions were trapped. These effects indicate that the sensitivity of detection of the trapped ions can be improved by appropriately choosing the pressure of the buffer gas and the sweep direction. The trapped ions could be detected until 76 h 20 min and the storage time of 1.3×10⁵ s was determined when these parameters were optimized.     

Calculation of the Storage Time of the Ions Confined in a Paul Trap

A Brownian motion model for the energy of the ions trapped in the pseudopotential well of a Paul trap is proposed and the exact solutions of the storage time in terms of the mean first passage time (MFPT) in the cases of white noises and colored noises are theoretically calculated. The relationships with the damping coefficient, noise parameters and the energy distribution of the ions are also discussed.     

Electrodynamic trap for neutral atoms

An electrodynamic trap is proposed that stores cold neutral atoms or nonpolar molecules in their ground state as well as in excited states by means of the quadratic Stark effect. The trap uses an oscillating hexapole field and a superposed static homogeneous field. The dynamics of an atom in this trap can be described as a harmonic oscillation in a static pseudopotential. Stability criteria and sample parameters for a number of atomic species are given. Received: 7 August 1998 / Received in final form: 7 January 1999     

Possible measurement of the gravitational acceleration of antiprotons in the presence of “strong” patch effect electrical fields

The role of electrical fields due to the patch effect in a Penning trap used to measure the Earth's gravitational accelerationg on antiprotons is analyzed. Theg measurement method is based on the study of the gravity-induced shift of the center of the radial orbits of particles stored in a Penning trap having the magnetic field perpendicular to the direction of the force of gravity. The analysis of the radial motion shows that forces originating from patch effect electrical fields about ten times stronger than the force of gravity, still allow a differential measurement ofg for antiprotons and matter particles (H^–). As the precision of the measurement is affected by the particle axial energy distribution, particular care must be devoted to injecting antiprotons and H^– ions into the trap with very similar initial conditions.     

Detection of Isotopes of Mercury Ions by Resonant Ejection in Paul Trap

A simple method to detect mercury ions confined in a Paul trap has been developed by resonant ejection. In this method, frequency of the additional ejection ac voltage is scanned instead of the amplitude of the rf drive voltage in conventional methods. It is possible not only to observe the spectra of the secular oscillation of the trapped ions directly, but also to eject the confined ions from the trap mass-selectively.     

Observation of a structural transition for Coulomb crystals in a linear Paul trap

A structural transition for laser cooled ion Coulomb crystals in a linear Paul trap just above the stability limit of parametrically resonant excitation of bulk plasma modes has been observed. In contrast to the usual spheroidal shell structures present below the stability limit, the ions arrange in a "string-of-disks" configuration. The spheroidal envelopes of the string-of-disks structures are in agreement with results from cold fluid theory usually valid for ion Coulomb crystals if the ion systems are assumed to be rotating collectively.     

Laser cooling of a small number of Be+ ions in a penning trap

Be⁺ ions stored in a Penning trap were cooled by a laser beam perpendicular to the magnetic field. The cooled ions are strongly coupled and phase transitions of up to 100 ions were observed. In experiments with only a few ions stored in the trap, a stepwise decrease in fluorescence intensity was observed. All steps are of the same size and so every step is attributed to a single ion. The discrete changes in fluorescence occurred more frequently when the background pressure was increased, caused by collisions between stored ions and background neutral molecules.     

Fluorescence Detection and Buffer Gas Cooling of Trapped Mercury Ions in Paul Trap

Pig ions are confined in a hyperboloid ion trap. With the rf discharge ^202 Hg isotope lamp, the fluorescence signal of trapped Hg ions is observed. By means of buffer gas cooling, the ionic temperature is reduced. As a result, the trapping time is increased and the signal-to-noise ratio （SNR） of the fluorescent signal is improved. The temperature of ion cloud is estimated by measuring the space charge shift.     

HITRAP: A Facility for Experiments with Trapped Highly Charged Ions

HITRAP is a planned ion trap facility for capturing and cooling of highly charged ions produced at GSI in the heavy-ion complex of the UNILAC-SIS accelerators and the ESR storage ring. In this facility heavy highly charged ions up to uranium will be available as bare nuclei, hydrogen-like ions or few-electron systems at low temperatures. The trap for receiving and studying these ions is designed for operation at extremely high vacuum by cooling to cryogenic temperatures. The stored highly charged ions can be investigated in the trap itself or can be extracted from the trap at energies up to about 10 keV/q. The proposed physics experiments are collision studies with highly charged ions at well-defined low energies (eV/u), high-accuracy measurements to determine the g-factor of the electron bound in a hydrogen-like heavy ion and the atomic binding energies of few-electron systems, laser spectroscopy of HFS transitions and X-ray spectroscopy. This revised version was published online in July 2006 with corrections to the Cover Date.     

Precise - and -factor measurements of Ba+ isotopes

Laser-microwave double and triple resonance experiments were performed on clouds of Ba⁺ ions confined in a Penning ion trap to induce and detect electronic and nuclear spin flip transitions. Collisions with buffer gas molecules in the trap was used to reduce the lifetime of a long lived metastable state of the ions, in which population trapping might occur, and to cool the ions to the ambient temperature. Loss of ions from the trap by collisions were prevented by coupling the magnetron and reduced cyclotron motions by an additional r.f. field at the sum frequency of the two motions. Electronic Zeeman transitions in ¹³⁸Ba⁺ and ¹³⁵Ba⁺ were observed at a full width of about 3 kHz at a transition frequency of 80 GHz. The uncertainty of the line center was . From the magnetic field calibration by the cyclotron resonance of electrons stored in the same trap the g_J-factor for both isotopes could be determined to . From radiofrequency induced transitions of ¹³⁵Ba⁺ the nuclear g-factor could be determined . Both measurements improve earlier results by about one order of magnitude. Received: 9 July 1998 / Accepted: 14 July 1998     

A compact Penning trap for light ions

We describe the construction of a novel compact Penning trap from strong permanent magnets for trapping light ions. Our cylindrically symmetric, iron-free magnetic configuration allows fully analytical treatment, is easy to handle and to optimize. The magnetic field inhomogeneity is less than 1% in a volume of 1 cm³ at 0.7 T. The stored H⁺ and H ₂ ⁺ ions in this trap are detected electrically by the rf absorption method. The charge density, total number and storage time of the trapped ions are measured.Dedicated to H. Walther on the occasion of his 60th birthday     

Sympathetic cooling of 4He+ ions in a radio-frequency trap

We have generated Coulomb crystals of ultracold 4He+ ions in a linear radio-frequency trap, by sympathetic cooling via laser-cooled 9Be+. Stable crystals containing up to 150 localized He+ ions at approximately 20 mK were obtained. Ensembles or single ultracold He+ ions open up interesting perspectives for performing precision tests of QED and measurements of nuclear radii. This Letter also indicates the feasibility of cooling and crystallizing highly charged atomic ions using 9Be+ as coolant.     

Linear Paul trap design for an optical clock with Coulomb crystals

We report on the design of a segmented linear Paul trap for optical clock applications using trapped ion Coulomb crystals. For an optical clock with an improved short-term stability and a fractional frequency uncertainty of 10^?18, we propose ¹¹⁵In⁺ ions sympathetically cooled by ¹⁷²Yb⁺. We discuss the systematic frequency shifts of such a frequency standard. In particular, we elaborate on high-precision calculations of the electric radiofrequency field of the ion trap using the finite element method. These calculations are used to find a scalable design with minimized excess micromotion of the ions at a level at which the corresponding second-order Doppler shift contributes less than 10^?18 to the relative uncertainty of the frequency standard.     

Kinetic Energy of Trapped Ions Cooled by Buffer Gas

The average kinetic energy of 40 Ca＋ ions is measured by the method of evaporating ions in an rf ion trap. The kinetic energy of the ion 40Ca＋ varies from 0.5eV to 0.2eV with changing buffer gas pressure from 10^-7 mbar to 10^-5 mbar. The Brownian motion model is also introduced to calculate the average kinetic energy of the trapped ions.     

Loading of large ion Coulomb crystals into a linear Paul trap incorporating an optical cavity

We report on the loading of large ion Coulomb crystals into a linear Paul trap incorporating a high-finesse optical cavity (?～3000). We show that, even though the 3-mm diameter dielectric cavity mirrors are placed between the trap electrodes and separated by only 12 mm, it is possible to produce in situ ion Coulomb crystals containing more than 10⁵ calcium ions of various isotopes and with lengths of up to several millimeters along the cavity axis. We show that the number of ions inside the cavity mode is, in principle, high enough to achieve strong collective coupling between the ion Coulomb crystal and the cavity field. The results thus represent an important step towards ion trap based Cavity Quantum ElectroDynamics (CQED) experiments using cold ion Coulomb crystals.