Using GPU parallelization to perform realistic simulations of the LPCTrap experiments

We performed classical molecular dynamics (MD) simulations in order to search the conditions for efficient sympathetic cooling of highly charged ions (HCIs) in a linear Paul trap. Small two-component ion Coulomb crystals consisting of laser-cooled ions and HCIs were characterized by the results of the MD simulations. We found that the spatial distribution is determined by not only the charge-to-mass ratio but also the space charge effect. Moreover, the simulation results suggest that the temperature of HCIs do not necessarily decrease with increasing the number of laser-cooled ions in the cases of linear ion crystals. We also determined the cooling limit of sympathetically cooled ¹⁶⁵Ho¹⁴⁺ ions in small linear ion Coulomb crystals. The present results show that sub-milli-Kelvin temperatures of at least 10 Ho¹⁴⁺ ions will be achieved by sympathetic cooling with a single laser-cooled Be⁺.     

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.     

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.     

Suitability of linear quadrupole ion traps for large Coulomb crystals

Growing and studying large Coulomb crystals, composed of tens to hundreds of thousands of ions, in linear quadrupole ion traps presents new challenges for trap implementation. We consider several trap designs, first comparing the total driven micromotion amplitude as a function of location within the trapping volume; total micromotion is an important point of comparison since it can limit crystal size by transfer of radiofrequency drive energy into thermal energy. We also compare the axial component of micromotion, which leads to first-order Doppler shifts along the preferred spectroscopy axis in precision measurements on large Coulomb crystals. Finally, we compare trapping potential anharmonicity, which can induce nonlinear resonance heating by shifting normal mode frequencies onto resonance as a crystal grows. We apply a non-deforming crystal approximation for simple calculation of these anharmonicity-induced shifts, allowing a straightforward estimation of when crystal growth can lead to excitation of different nonlinear heating resonances. In the anharmonicity point of comparison, we find significant differences between the trap designs, with an original rotated-endcap trap performing better than the conventional in-line endcap trap.     

Compensating for excess micromotion of ion crystals

A new method of compensating for the excess micromotion along two directions in three-dimensional Coulomb crystals is reported in this paper; this method is based on shape control and optical imaging of a Coulomb crystal in a sectioned linear ion trap. The characteristic parameters, such as the ion numbers, temperatures, and geometric factors of different ion crystals are extracted from the images and secular motion excitation spectra. The method of controlling the shape of the ion crystals can be used in cold ion experiments, such as sympathetically cooling, structural phase transitions,and selective-control of ions, etc.     

Photon-trap spectroscopy of size-selected free cluster ions: “direct” measurement of optical absorption of Ag+ 9

An absorption spectrum of size-selected free cluster ions has been measured “directly” via extinction of light without relying on photodepletion/dissociation spectroscopy. The novel technique employs an ion trap and an optical cavity; cluster ions stored in an ion trap interact with photons trapped in a cavity. The storage lifetime of photons in the cavity provides “direct” observation of extinction of light (photon-trap spectroscopy, which is a generalized scheme of cavity ring-down spectroscopy). The first measurement is performed on ultraviolet absorption of Ag₉ ⁺. Temperature dependence of the spectrum is presented by cooling the ion trap down to 10 K.     

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.     

Cold ion chemistry within Coulomb crystals

Coulomb crystals are ordered structures of spatially-localised ions, held within an ion trap and exhibiting very low translational temperatures. The many advantages of studying the spectroscopic, kinetic and dynamic properties of gas phase ions in Coulomb crystals – such as the ability to manipulate and detect single ions under ultrahigh vacuum conditions – have seen their adoption in an ever-expanding range of fields. This article provides an overview of recent developments, where Coulomb crystals have been utilised for precision measurements, for the study of controlled ion-neutral reactions and in the implementation of quantum information science.     

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.     

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.     

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.     

Isotope selective loading of an ion trap using resonance-enhanced two-photon ionization

We have demonstrated that resonance-enhanced two-photon ionization of atomic beams provides an effective tool for isotope selective loading of ions into a linear Paul trap. Using a tunable, narrow-bandwidth, continuous wave (cw) laser system for the ionization process, we have succeeded in producing Mg⁺ and Ca⁺ ions at rates controlled by the atomic beam flux, the laser intensity, and the laser frequency detuning from resonance. We have observed that with a proper choice of control parameters, it is rather easy to load a specific number of ions into a string. This observation has direct applications in quantum optics and quantum computation experiments. Furthermore, resonant photo-ionization loading facilitates the formation of large isotope-pure Coulomb crystals. Received: 21 December 1999 / Published online: 11 May 2000     

A thin wire ion trap to study ion–atom collisions built within a Fabry–Perot cavity

We report on the implementation of a thin wire Paul trap with tungsten wire electrodes for trapping ions. The ion trap geometry, though compact, allows large optical access enabling a moderate finesse Fabry–Perot cavity to be built along the ion trap axis. The design allows a vapor-loaded magneto-optical trap of alkali atoms to be overlapped with trapped atomic or molecular ions. The construction and design of the trap are discussed, and its operating parameters are determined, both experimentally and numerically, for Rb⁺. The macromotion frequencies of the ion trap for ⁸⁵Rb⁺ are determined to be f _r  = 43 kHz for the radial and f _z  = 54 kHz for the axial frequencies, for the experimentally determined optimal operating parameters. The destructive off axis ion extraction and detection by ion counting is demonstrated. Finally, evidence for the stabilization and cooling of trapped ions, due to ion–atom interactions, is presented by studying the ion-atom mixture as a function of interaction time. The utility and flexibility of the whole apparatus, for a variety of atomic physics experiments, are discussed in conclusion.     

Mode shaping in mixed ion crystals of 40Ca2+ and 40Ca+

We present studies of mixed Coulomb crystals of ⁴⁰Ca⁺ and ⁴⁰Ca²⁺ ions in a linear Paul trap. Doubly charged ions are produced by photoionization of trapped ⁴⁰Ca⁺ with a vacuum ultraviolet laser source and sympathetically cooled via Doppler cooled ⁴⁰Ca⁺ ions. We investigate experimentally and theoretically the structural configurations and the vibrational modes of these mixed crystals. Our results with ⁴⁰Ca²⁺ are an important step towards experimental realization of the proposals for mode shaping in a linear crystal and spin-dependent configuration changes from zigzag to linear as proposed by Li et al. (Phys Rev A 87:052304, 2013) and Li and Lesanovsky (Phys Rev Lett 108:023003, 2012) using ions excited to Rydberg states.     

Coulomb expansion of laser-excited ion plasmas

We determine the electric field in mm-sized clouds of cold Rb+ ions, produced by photoionization of laser-cooled 87Rb atoms in a magneto-optical trap, using the Stark effect of embedded Rydberg atoms. The dependence of the electric field on the time delay between the ion plasma production and the probe of the electric field reflects the Coulomb expansion of the plasma. Our experiments and models show expansion times <1micros.     

线型离子阱中空间电荷效应的理论分析

线型离子阱中的离子在射频场作用下做宏观的久期运动,久期运动频率与实验参数有关.但当离子阱中囚禁大量同种电荷的离子时,空间电荷效应会导致离子间存在相互排斥的库仑力,使离子的运动频率发生漂移.本文通过求解泊松方程计算了空间电荷产生的附加电场的解析表达式,在小振动近似下理论计算了该附加电场对久期运动频率的影响,模拟了不同离子云中心密度下久期频率的漂移,讨论了离子云的数目、温度与实验参数之间的关系.对用离子阱进行的频标实验、碰撞实验和其他方面的研究都具有重要的指导意义.     

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.     

First stage f centre formation in pure and doped KCl crystals by room temperaure X-irradiation

The electrical conductivity and optical absorption of potassium chloride crystals, pure and doped with divalent cation impurities, have been measured before and after X-irradiation at room temperature. The concentration of free positive ion vacancies at room temperature has been calculated from conductivity for each crystal before irradiation and is found to be much less than the first stage F centre concentration. This shows that both free and associated positive ion vacancies are the latent source of F centres in the first stage colouration. Pb^{+ +} ions trap electrons producing Pb^{+ +} and Pb⁰ centres and making free the associated cation vacancies. Such centres are not produced in Ca-doped crystals where impurity-vacancy complexes trap F centres producing Z centres. The higher ratio of F centres to positive ion vacancies in Pb-doped crystals indicates that free cation vacancies are more effective in producing F centres. However, the concentration of divalent cations is found to decrease in both the crystals after irradiation, the decrease being more in Ca-doped crystals.The author is indebted to Prof. H. N. Bose for helpful discussions. Thanks are also due to Dr. M. L. Mukherjee for providing the crystals.     

All-diode-laser cooling of single Ca+ ions

+ ions. The Ca⁺ ions are trapped in a miniature rf Paul trap and irradiated by light from a frequency-doubled diode laser at 397 nm and by light from a diode laser at 866 nm. We are able to cool a single ion and observe its fluorescence continuously with the laser diode locked to the external frequency-doubling cavity. Quantum jumps in the fluorescence light of a single ion and of a small cloud of five ions have been induced by driving the “clock” transition at 729 nm. We were able to resolve the influence of the micromotion on the excitation spectrum of the small ion cloud. Received: 10 July 1997/Revised version: 17 November 1997