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.     

Simulating the stopping dynamics of highly charged ions in an ultra-cold, strongly coupled plasma

We introduce a method for stopping highly charged ions (HCIs) in a laser-cooled one-component plasma (OCP) of ²⁴Mg⁺ ions and present results on stopping times derived from realistic molecular dynamics simulations of the complete stopping process. This stopping scheme can provide ultra-cold highly charged ions for future in-trap precision mass measurements. The choice of an ultra-cold ion plasma as a stopping medium is governed by the almost negligible charge exchange of the HCI with the laser-cooled ions and the very low temperatures which can be reached. In our analysis we focus on the stability and fast recooling of the plasma – two features essential for the experimental realization of this stopping scheme.      

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.     

Dissociative ionization of the H2O molecule bombarded by swift singly charged and slow highly charged ions

Fragment ion energy spectra of the water molecule have been measured in conventional crossed-beam experiments by the impact of 46 keV/u energy, singly charged ions (SCIs) and 4.3 keV/u energy, highly charged ions (HCIs). Double differential cross sections have been determined and a comparative analysis has been performed. We found that the fragmentation spectra for SCIs and HCIs are very similar, indicating that both collisions lead to the same fragmentation channels. This suggests that the Coulomb explosion of the water molecule is dominantly determined by the charge state of the transient molecular ions, and it is almost independent from the primary ionization mechanism. Differences were observed not only between the SCI and HCI impact-induced fragmentation cross sections, but between those obtained by the 60 keV N⁶⁺ and 70 keV O⁷⁺ projectiles. The differences were attributed to the selectivity of the electron capture process for HCIs. Multiple target ionization cross sections have been deduced from the fragment ion spectra. We found contributions of up to fivefold ionization for SCIs and up to sixfold ionization for HCIs.     

Production of ultracold trapped molecular hydrogen ions

We have cooled ensembles of the molecular hydrogen ions H2+, H3+, and all their deuterated variants to temperatures of a few mK in a radio frequency trap, by sympathetic cooling with laser-cooled beryllium ions. The molecular ions are embedded in the central regions of Coulomb crystals. Mass spectroscopy and molecular dynamics simulations were used to accurately characterize the properties of the ultracold multispecies crystals. We demonstrate species-selective purification of multispecies ensembles. These molecules are of fundamental importance as the simplest of all molecules, and have the potential to be used for precision tests of molecular structure theory, tests of Lorentz invariance, and measurements of electron to nuclear mass ratios and their time variation.     

Sympathetic cooling rate of gas-phase ions in a radio-frequency-quadrupole ion trap

We theoretically investigated the mass dependence of the sympathetic cooling rate of gas-phase ions trapped in a linear radio-frequency-quadrupole ion trap. Using an a priori molecular dynamical calculation, tracing numerically with Newtonian equations of motion, we found that ions with a mass greater than 0.54±0.04 times that of the laser-cooled ions are sympathetically cooled; otherwise, they are heated. To understand the mass dependence obtained using the molecular-dynamical calculation, we made a heat-exchange model of sympathetic cooling, which shows that the factor of 0.54±0.04 is a consequence of absence of micro-motion along the axis of the linear ion trap. Received: 10 December 2001 / Revised version: 28 January 2002 / Published online: 14 March 2002     

Ion crystals in a linear Paul trap

Large ion crystals containing as many as 10⁵ laser-cooled 24Mg⁺ ions arranged in 10 cylindrical shells around a central string have been observed in a linear Paul trap. For smaller crystals consisting of approximately 3500 ions, the varying linear charge densities along the trap axis give rise to well-defined transition regions between the different shell-structures. These structures and the transition regions as a function of linear density are in good agreement with molecular dynamics simulations. The micromotion of the ions in such smaller crystals is also investigated through comparison with MD-simulations. Finally, the degree and progression of ordering in the plasma have been observed for various temperatures and compared with MD-simulations. Good qualitative agreement is again obtained. This revised version was published online in July 2006 with corrections to the Cover Date.     

Molecular self-organization of Ho<Superscript>3+</Superscript> impurity ions in synthetic forsterite

The structure of paramagnetic centers formed by impurity Ho³⁺ ions in synthetic forsterite is studied by submillimeter EPR spectroscopy in the frequency range 65–200 GHz. It is found that Ho³⁺ enters into the Mg²⁺ sublattice in the form of single ions and dimer centers. The concentration of dimer centers considerably exceeds the concentration of single ions, which points to the molecular self-organization of Ho³⁺ impurity ions into dimers during the growing of the crystals from melt. Possible structures of the dimer center are discussed. The parameters of the effective spin Hamiltonian describing the behavior of the electron-nuclear sublevels of the two lowest electronic levels of the Ho³⁺⁵I₈ ground multiplet are determined for a single ion and a dimer center.     

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.     

Observation of three-dimensional long-range order in small ion coulomb crystals in an rf trap

Three-dimensional long-range ordered structures in smaller and near-spherically symmetric Coulomb crystals of (40)Ca(+) ions confined in a linear rf Paul trap have been observed when the number of ions exceeds approximately 1,000 ions. This result is unexpected from ground state molecular dynamics (MD) simulations, but found to be in agreement with MD simulations of metastable ion configurations. Previously, three-dimensional long-range ordered structures have only been reported in Penning traps in systems of approximately 50,000 ions or more.     

Cold highly charged ions in a cryogenic Paul trap

Narrow optical transitions in highly charged ions (HCIs) are of particular interest for metrology and fundamental physics, exploiting the high sensitivity of HCIs to new physics. The highest sensitivity for a changing fine structure constant ever predicted for a stable atomic system is found in Ir^17?+?. However, laser spectroscopy of HCIs is hindered by the large (～ 10⁶ K) temperatures at which they are produced and trapped. An unprecedented improvement in such laser spectroscopy can be obtained when HCIs are cooled down to the mK range in a linear Paul trap. We have developed a cryogenic linear Paul trap in which HCIs will be sympathetically cooled by ⁹Be^?+? ions. Optimized optical access for laser light is provided while maintaining excellent UHV conditions. The Paul trap will be connected to an electron beam ion trap (EBIT) which is able to produce a wide range of HCIs. This EBIT will also provide the first experimental input needed for the determination of the transition energies in Ir^17?+?, enabling further laser-spectroscopic investigations of this promising HCI.     

Significantly Improving the Escape Time of a Single ~(40)Ca~+ Ion in a Linear Paul Trap by Fast Switching of the Endcap Voltage

Sympathetic cooling is a method used to lower the kinetic energy of ions with complicated energy-level structures,via Coulomb interactions with laser-cooled ions in an ion trap.The ion to be sympathetically cooled is sometimes prepared outside of the trap,and it is critical to introduce this ion into the trap by temporarily lowering the potential of one endcap without allowing the coolant ion to escape.We study the time required for a laser-cooled ion to escape from a linear Paul trap when the voltage of one endcap is lowered.The escape time is on the order of a few microseconds,and varies significantly when the low-level voltage changes.A re-cooling time of a maximum of 13 s was measured,which can be reduced to approximately one hundred of milliseconds by decreasing the duration of the low-level voltage.The measurement of these critical values lays the foundation for the smooth injection and cooling of the ion to be sympathetically cooled.     

Up-conversion emission in triply-doped Ho/Yb/Tm KGd(WO4)2 single crystals

Detailed spectroscopic studies of the triply doped KGd(WO₄)₂:Ho³⁺/Yb³⁺/Tm³⁺ single crystals (which exhibit multicolor up-conversion fluorescence) are reported for the first time. The absorption spectra of crystals were measured at 10 and 300 K; the room temperature luminescence spectra were excited at 980 nm wavelength. The dependence of the intensity of luminescence on the excitation power for three different concentration of Ho³⁺, Yb³⁺ and Tm³⁺ ions was investigated. Efficient green and red up-converted luminescence of Ho³⁺ ions and weak blue up-conversion luminescence of Tm³⁺ ions were observed in spectra. The red emission of Ho³⁺ ions is more intensive than their green emission. Dependence of the up-conversion luminescence intensity on the excitation power and impurities concentration was also studied; the number of phonon needed for efficient up-conversion was determined for each case. All possible energy transfer processes between different pairs of the impurity ions' energy levels are also discussed.     

Multifrequency EPR spectroscopy of Ho3+ ions in synthetic forsterite

Electron paramagnetic resonance (EPR) of Ho³⁺ single ions and Ho³⁺?Mg²⁺-vacancy-Ho³⁺ associates in holmium-doped forsterite single crystals are studied at 9.4, 37.3 and 65–250 GHz. Crystals were grown from melt by the Czochralski technique in slightly oxidizing atmosphere. For both centers, directions of the principal magnetic axes and parameters of the effective spin Hamiltonians describing dependences of electron-nuclear levels on applied magnetic field are obtained. For Ho³⁺ substituting Mg²⁺ in the M2 site as the single ion and for Ho³⁺ ions in dimer centers, values of crystal field parameters related to a real crystal lattice structure are estimated in the framework of the exchange charge model. The calculated crystal field energies, values of theg-factors of the ground Ho³⁺ quasi-doublet and the directions of the corresponding magnetic moments agree satisfactorily with the data obtained from measurements of EPR and optical absorption and site-selective luminescence spectra.     

Numerical analysis of motional mode coupling of sympathetically cooled two-ion crystals

A two-ion pair in a linear Paul trap is extensively used in the research of the simplest quantum-logic system; however,there are few quantitative and comprehensive studies on the motional mode coupling of two-ion systems yet. This study proposes a method to investigate the motional mode coupling of sympathetically cooled two-ion crystals by quantifying three-dimensional(3 D) secular spectra of trapped ions using molecular dynamics simulations. The 3 D resonance peaks of the ~(40)Ca~+ – ~(27)Al~+ pair obtained by using this method were in good agreement with the 3 D in-and out-of-phase modes predicted by the mode coupling theory for two ions in equilibrium and the frequency matching errors were lower than 2%.The obtained and predicted amplitudes of these modes were also qualitatively similar. It was observed that the strength of the sympathetic interaction of the ~(40)Ca~+ – ~(27)Al~+ pair was primarily determined by its axial in-phase coupling. In addition,the frequencies and amplitudes of the ion pair's resonance modes(in all dimensions) were sensitive to the relative masses of the ion pair, and a decrease in the mass mismatch enhanced the sympathetic cooling rates. The sympathetic interactions of the ~(40)Ca~+ – ~(27)Al~+ pair were slightly weaker than those of the ~(24)Mg~+– ~(27)Al~+ pair, but significantly stronger than those of ~9Be~+ – ~(27)Al~+ . However, the Doppler cooling limit temperature of ~(40)Ca~+ is comparable to that of ~9Be~+ but lower than approximately half of that of ~(24)Mg~+. Furthermore, laser cooling systems for ~(40)Ca~+ are more reliable than those for ~(24)Mg~+and ~9Be~+ . Therefore, ~(40)Ca~+ is probably the best laser-cooled ion for sympathetic cooling and quantum-logic operations of ~(27)Al~+ and has particularly more notable comprehensive advantages in the development of high reliability, compact, and transportable ~(27)Al~+ optical clocks. This methodology may be extended to multi-ion systems, and it will greatly aid efforts to control the dynamic behaviors of sympathetic cooling as well as the development of low-heating-rate quantum logic clocks.     

Laser-polarimetric measurements of magnetic ac-susceptibility in LiYF<Subscript>4</Subscript>: Ho<Superscript>3+</Superscript> crystals

Laser-polarimetric technique with the shot-noise-limited polarimetric sensitivity is used to study magnetic ac-susceptibility in holmium doped LiYF₄ crystals in the range of Zeeman energies comparable with that of the hyperfine interaction in Ho³⁺ ions. Specific features of optical methods of magnetic measurements, the experimental setup, and results of measurements are discussed. Polarimetric sensitivity of the setup (～10^?8 rad) allowed us to measure the ac-susceptibility of LiYF₄ single crystals containing 0.1–0.3 mol % of impurity Ho³⁺ ions with the signal-to-noise ratio exceeding 10². The obtained field-strength and frequency dependences of the ac-susceptibility show that the resonant peaks of the susceptibility mainly result from cross-relaxation transitions between the electronic-nuclear sublevels of Ho³⁺ ions.     

Hypersensitive transitions of Tm3+, Ho3+ and Dy3+ rare-earth ions in garnet crystals

In this work, spectroscopic characteristics (oscillator strengths, intensity parameters) of intermanifold f–f transitions of Tm^{3 +}, Ho³⁺and Dy³⁺ions in garnet crystals are investigated. It has been found that the intensity change of the hypersensitive intermanifold f–f transitions of rare-earth ions in garnet crystals is determined by the characteristics of their local environment.     

Highly charged ion Coulomb crystallization in mixed strongly coupled plasmas

The investigation of highly charged ion Coulomb crystallization in mixed strongly coupled plasmas is of interest in many areas: white dwarf astrophysical plasmas are believed to have very similar thermodynamic properties, cold highly charged ions can be used as an object for high precision laser spectroscopy of fine and hyperfine transitions in the visible due to the absence of Doppler broadening and, an entirely new area of research is the potential application to highly charged ion based quantum computing schemes. We report the formation of such plasmas in a cryogenic Penning trap. These plasmas consisting of many species including Be⁺ and Xe⁴⁴⁺ or Be⁺ and Xe¹⁵⁺ ions, are formed at a temperature of less than 4 K. The temperatures were obtained by applying a laser based sympathetic cooling scheme. The determination of the temperature and density from the laser resonance width and the fluorescence imaging of the Be⁺ clouds, respectively, yields a Coulomb coupling constant for the centrifugally separated Xe plasma high enough for crystallization. A molecular dynamics code, developed just for this purpose, was run to clarify the understanding of these plasmas and it was possible to show consistency between experiment and simulation. This revised version was published online in August 2006 with corrections to the Cover Date.     

Microfabricated surface-electrode ion trap for scalable quantum information processing

Individual laser-cooled 24Mg+ ions are confined in a linear Paul trap with a novel geometry where gold electrodes are located in a single plane and the ions are trapped 40 microm above this plane. The relatively simple trap design and fabrication procedure are important for large-scale quantum information processing (QIP) using ions. Measured ion motional frequencies are compared to simulations. Measurements of ion recooling after cooling is temporarily suspended yield a heating rate of approximately 5 motional quanta per millisecond for a trap frequency of 2.83 MHz, sufficiently low to be useful for QIP.     

Characteristics of highly charged ions produced at Kobe EBIS under modulated operation

The electron beam ion source (Kobe EBIS) has been developed to perform modification of surfaces using highly charged ions (HCIs) at the Kobe University, Japan. Recent study revealed that periodic intermission of electron beam improves charge state distribution of extracted ions. The period of intermission is in the order of 100 ms, and the width of beam-off time is 1 ms or less. This operational mode (pulse mode) makes it possible to produce Ar¹⁵⁺ to Ar¹⁷⁺ effectively, whereas the charge is limited less than 14+ under the ordinary operational mode with direct current (DC) electron beam. A spike of HCIs with a peak current in the order of nA is also observed at each moment of electron beam off. The measurement of the time evolution of Ar¹⁶⁺ intensity around the timing of mode change revealed that the intensity of extracted Ar¹⁶⁺ changes slowly after mode change with a time constant of few seconds.