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.     

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.     

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.     

Structure and control of Coulomb crystals in a Penning trap

We apply rotating electric fields to ion plasmas in a Penning trap to obtain phase-locked rotation about the magnetic field axis. These plasmas, containing up to 10^{6 9}Be⁺ ions, are laser-cooled to millikelvin temperatures so that they freeze into solids. Single body-centered cubic (bcc) crystals have been observed by Bragg scattering in nearly spherical plasmas with ≳ 2 × 10⁵ ions. The detection of the Bragg patterns is synchronized with the plasma rotation, so individual peaks are observed. With phase-locked rotation, the crystal lattice and its orientation can be stable for longer than 30 min or ∼10⁸ rotations. This revised version was published online in July 2006 with corrections to the Cover Date.     

Observation of instabilities in a Paul trap with higher-order anharmonicities

Systematic measurements of the relative ion number stored in a Paul trap within the stability diagram given by the solution of the equation of motion reveal many lines, where only few or no ions can be confined. The observations can be explained by the presence of perturbations from higher-order components in the trapping potential, which is a quadrupole potential in the ideal case. The resonances follow the equation (n _r /2) _r + (n _r /2) _z = 1,n _r +n _z =N, where 2N is the order of the perturbation,n _r ,n _z are integer and _r , _z are stability parameters of the trap. The experiments were performed on H⁺ and H ₂ ⁺ ions, which are detected after a storage time of 0.3 s by ejection from the trap.     

A linear Paul trap for radiative lifetime measurements on ions

A linear ion trap has been designed for collimation and storage of ions from an effusive particle beam generated in a hollow cathode discharge. The motivation is to measure radiative lifetimes on multiply ionized atoms by using the time-resolved laser-induced fluorescence technique. The trap has been tested on iron and tungsten ions both as an ion guide and also as a storing device. Radiative lifetimes have been measured in the trap with a remarkably higher signal-to-noise ratio than in the original effusive atom beam.     

Quantum control of 88Sr+ in a miniature linear Paul trap

We report on the construction and characterization of an apparatus for quantum information experiments using ⁸⁸Sr⁺ ions. A miniature linear radio-frequency (rf) Paul trap was designed and built. Trap frequencies above 1 MHz in all directions are obtained with 50 V on the trap end-caps and less than 1 W of rf power. We encode a quantum bit (qubit) in the two spin states of the S _1/2 electronic ground-state of the ion. We constructed all the necessary laser sources for laser cooling and full coherent manipulation of the ions’ external and internal states. Oscillating magnetic fields are used for coherent spin rotations. High-fidelity readout as well as a coherence time of 2.5 ms are demonstrated. Following resolved sideband cooling the average axial vibrational quanta of a single trapped ion is $\bar{n}=0.05$ and a heating rate of $\dot{\bar{n}}=0.016~\mathrm{ms}^{-1}$ is measured.     

Axial resonances of Ar + ions observed in a linear Paul trap

Non-neutral plasmas composed of 10⁶ to 10⁷ Ar⁺ ions were confined in a linear Paul trap which had a non-harmonic electrostatic potential in axial direction. Axial resonances were observed by applying additional RF electric field and detecting axially ejected ions. It was found that the resonance frequencies shifted as a function of the ion number, the amplitude of additional RF electric field, and the applied electrostatic potential for the axial confinement.      

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.     

Charge interaction in a Paul trap

In third order perturbation theory we obtained the expression for an averaged Hamiltonian describing the classical motion of two particles in a Paul trap. The arising small corrections are interpreted as mass and charge renormalization.     

Nonlinear resonances and phase transitions of two-ion Coulomb clusters in a Paul trap: Calculations without laser cooling

The mechanism responsible for transitions of laser-cooled trapped ions from an ordered crystal state to an irregular cloud state has been discussed controversially. A numeric and analytic study of the relative motion of two trapped ions without laser cooling is performed and compared with the results of previous simulations involving the laser. It turns out that the system without laser, in spite of its simplicity, already exhibits a non-monotonic dependence of crystal stability on trap parameters, which is linked to the presence of low-order nonlinear resonances.     

Solitary waves in a long structure of charged particles confined in the linear Paul trap

This paper demonstrates the possibility of generation of density waves in the form of individual humps in a long structure of the one-component Coulomb system of dust particles confined in the linear Paul traps in air under normal conditions Our numerical simulations by particle-in-cell method support this possibility. Physical possibility of analogous the hump density waves (caustics) is discussed by V.I. Arnold in his book ‘Catastrophe Theory’ and is caused by the nonuniform velocity distribution of dust particles.     

Separation of laser-cooled 42Ca+ and 44Ca+ in a linear Paul trap

Rare calcium isotope ions, ⁴²Ca⁺ and ⁴⁴Ca⁺, were efficiently separated from a laser-cooled ionic cloud in a linear Paul trap which was loaded from an atomic source of a natural isotope mixture of calcium, in spite of their negligibly small abundances (0.647% and 2.086%, respectively) compared with that of ⁴⁰Ca (96.94%). Selective heating and cooling that arise from the isotope shifts were mainly used for the elimination of the isotopes; selective heating and cooling enable flexible separation when combined with other mechanisms such as the inherent mass selectivity of RF traps. Received: 7 July 2000 / Published online: 10 January 2001     

Self-induced zeeman coherences in a Paul trap

A new method for the measurement of motional frequencies and amplitudes of stored ions in a radio-frequency trap is presented. Ions oscillating in the trap potential and additionally subjected to a small magnetic field, undergo sublevel transitions between adjacent Zeeman states when their motional frequency is identical with the Larmor frequency in the applied magnetic field. These transitions can be sensitively detected by means of an optical pumping scheme. As they are related to a coherent superposition of adjacent states and originate from the inherent motion of the ions in a slightly inhomogeneous magnetic field, this phenomenon is termed self-induced Zeeman coherence.     

Laser cooling and isotope separation of Cd(+) ions conf ined in a linear Paul trap

Cadmium ions in a natural isotope mixture have been trapped in a linear Paul trap and laser cooled. The fluorescence spectra from all even isotopes, including the (108)Cd(+) isotopes with a natural abundance of 0.89%, were observed. Additionally, we eliminated the heavier isotopes from the trapping region by adjusting the tuning of the laser frequency and by changing the dc voltage applied to the end electrodes.     

Continuous quantum measurements of a particle in a Paul trap

We calculate the propagator of a particle caught in a Paul trap and subject to the continuous quantum measurement of its position. The probabilities of the measurement outputs, the possible trajectories of the particle, are also found. This enables us to propose a series of experiments that would allow us to compare the predictions of one of the models that describe the interaction between a measured quantum system and measuring device, namely the so-called restricted path-integral formalism, with the experiment.