I. Siemers

Brownian motion of a parametric oscillator: A model for ion confinement in radio frequency traps

The distribution function for Brownian motion of a parametric oscillator is calculated exactly with the help of continued fraction expansions in the long time limit. We derive expressions for the energy and the widths of the spatial and velocity distribution. Our results are relevant to understand confinement of particles in radio frequency ion traps.

On the photo-dynamics of single ions in a trap

Early this century, atomic beams were the closest approach tofree atomic particles. Nowadays, individual ions are stored in traps for, in principle, unlimited times of experimentation. The recoil of absorbed or scattered light permits us to manipulate the ion kinetics: Cooling and heating the ion reveals novel types of nonlinear light forces, one of which results from an all-stimulated parametric process similar to the action of a free-electron laser. — The amplitude of the vibration of a single ion in the potential well of the trap locks to metastable levels of excitation. Few ions form crystals or rotating quasi-molecules. Random exchange of sites is demonstrated by a quasi-molecule composed of a fluorescing and a dark ion.

Quantized infrared-optical triple resonance on a single cold barium ion

A single trapped and cooled Ba+ ion is irradiated by resonant visible light (493, 650 nm) alternating with light at 1.76 µm which may excite the ion to its2D5/2 metastable state. The (absence of) visible resonance scattering probes the excitation, tuning spectra of which show vibrational sidebands that characterize the ions temperature. Observed values as low as 120 µK, one-eighth the Doppler limit, are ascribed to electronic Raman cooling by the visible light. Tuning spectra of the events of stimulated deexcitation indicate ion heating by the IR interaction. The results demonstrate the feasibility of vibrational spectrometry on a single particle that oscillates in a potential well, forming a quasi-molecule.

Kinetic energy and spatial width of ion clouds in Paul traps

The ratio of the mean kinetic energy and the spatial width of ion clouds in Paul traps has been measured. The result is compared with predictions of various models that describe ion cloud dynamics in Paul traps.

Light shift and Fano resonances in a single cold ion

The simultaneous excitation of adjacent atomic transitions by two light waves equally detuned from their resonances gives rise to destructive interference of the transitions and causes a narrow dark line, or coherent dip, to appear in both light scattering and absorption. With one of the light fields detuned from resonance, the line is asymmetric and is accompanied by a shifted bright line; the two are represented by a Fano line profile. The spectral separation ∊ of the bright and dark lines is closely related—although not identical—to the net shift that is found in the two-photon-resonant denominator of the susceptibility, to the shift of the normal modes of the atom’s two internal excitations, and to the net difference of the energy separations of dressed and bare atomic levels. We report measurement of the resonance shift ∊ of the 2S1/2–2D3/2 transition of a single cooled and trapped Ba+ ion, and we analyze its relationship to those identified light shifts.

Motional Stability of a Nonlinear Parametric Oscillator: Ion Storage in the RF Octupole Trap

We demonstrate confinement of ion clouds in a radio-frequency anharmonic electric potential and investigate the stability of this nonlinear parametric oscillator. Measurements of excitation spectra and the spatial distribution of trapped ion clouds are presented. Further applications of r.f. multipole traps to high-resolution spectroscopy are discussed.

Spatially localized optical pumping in Paul traps

Spatially localized optical pumping into energy eigenstates and into a long-living nonabsorbing coherent superposition of the two low-lying metastable states of the Ba+ ion has been observed. The spatial localization is traced to the properties of micromotion in Paul traps. Observed spatial distributions of the laser-induced fluorescence have been qualitatively reproduced by using a model based on the notion of velocity amplitudes and the Brownianmotion model of ion dynamics in the Paul trap.

The Kinetic Energy of Ion Clouds in Paul Traps

The dynamics of ion clouds in Paul traps has been experimentally investigated. Kinetic energy and the width of the spatial distribution of ions has been measured. Their dependence on the traps operating conditions is compared with the results of a recent model calculation based on Brownian motion.

Optical double-resonance on single cold ions

Resonance on a weak signal line of a single cold ion appears at the maximum rate of intermittent quenching the fluorescence on a resonance line: The m=0/spl rarr/0 ground state hyperfine transition of a single /sup 171/Yb/sup +/ and the S/sub 1/2 /-D/sub 5/2/ quadrupole line of /sup 138/Ba/sup +/ may control a 12.6-GHz oscillator or 1.76-/spl mu/m laser, respectively, with less than 10/sup -16/ inaccuracy.<<ETX>>

Kinetic Energy and Spatial Distribution of Ion Clouds in Paul Traps

Ion traps provide a very favourable environment for the conduction of experiments aimed at high spectral resolution: They allow the preparation of ionic samples localized in space free of collisions with walls [1]. In this situation, the second order Doppler effect is the largest systematic error, which can be reduced by laser cooling of the stored ions [2]. However, this merely works with few ions and yields only low signal-to-noise ratio. Another approach is to measure or to calculate the second-order Doppler effect and to hold it constant. In order to do so, an investigation of the dynamics of ion clouds has been performed. The ions’ motion is described as Brownian motion in the time-dependent trapping potential. Both damping and diffusion terms due to collisions with the background gas and other ions are introduced on a phenomenological basis. The corresponding Fokker-Planck-equation has been solved analytically and results in the joint distribution of position and velocity as a function of the trap parameters. This Gaussian distribution has time-dependent variances and shows a correlation between position and velocity. With that, the mean kinetic energy can be calculated and a correction for the second-order Doppler effect can be extracted [3].