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arXiv:0902.2746 · Journal of Physics B Atomic Molecular and Optical Physics

About the dynamics and thermodynamics of trapped ions

C. Champenois

Published Jul 15, 2009• 34 citations
arXivHTMLPDF

Abstract

This paper introduces the dynamics of charged particles in a radiofrequency trap in a very general manner to point out the differences between the dynamics in a quadrupole and in a multipole trap. When dense samples are trapped, the dynamics is modified by the Coulomb repulsion between ions. To take into account this repulsion, we propose to use a method, originally developed for particles in a Penning trap, that models the ion cloud as a cold fluid. This method can not reproduce the organization of cold clouds as crystals but it allows one to scale the size of large samples with the trapping parameters and the number of trapped ions, for different linear geometries of trap.

DOI
10.1088/0953-4075/42/15/154002

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This paper introduces the dynamics of charged particles in a radiofrequency trap in a very general manner to point out the differences between the dynamics in a quadrupole and in a multipole trap. When dense samples are trapped, the dynamics is modified by the Coulomb repulsion between ions. To take into account this repulsion, we propose to use a method, originally developed for particles in a Penning trap, that models the ion cloud as a cold fluid. This method can not reproduce the organization of cold clouds as crystals but it allows one to scale the size of large samples with the trapping parameters and the number of trapped ions, for different linear geometries of trap.
Abstract. While the linear radiofrequency trap finds various applications in high-precision spec-troscopy and quantum information, its higher-order cousin, the linear multipole trap, is almost exclu-sively employed in physical chemistry. Recently, first experiments have shown interesting features by laser-cooling multipole-trapped ion clouds. Multipole traps show a flatter potential in their cen-tre and therefore a modified density distribution compared to quadrupole traps. Micromotion is an important issue and will certainly influence the dynamics of crystallized ion structures. Our experi-ment tends to investigate possible crystallization processes in the multipole. In a more general way, we are interested in the study of the dynamics and thermodynamics of large ion clouds in traps of different geometry.
While the linear radiofrequency trap finds various applications in high-precision spectroscopy and quantum information, its higher-order cousin, the linear multipole trap, is almost exclusively employed in physical chemistry. Recently, first experiments have shown interesting features by laser-cooling multipole-trapped ion clouds. Multipole traps show a flatter potential in their centre and therefore a modified density distribution compared to quadrupole traps. Micromotion is an important issue and will certainly influence the dynamics of crystallized ion structures. Our experiment tends to investigate possible crystallization processes in the multipole. In a more general way, we are interested in the study of the dynamics and thermodynamics of large ion clouds in traps of different geometry.
The quadrupole linear Paul trap is one of the key instruments in building highly stable atomic clocks. However, a frequency reference based on a single trapped ion is limited in stability due to the time needed for the interrogation cycle which cannot be further shortened. A promising strategy is the utilization of multiple trapped ions. The ions of the same kind then repulse each other with the Coulomb force, which is countered by the ponderomotive force of the time depended field in the trap. A few ions form a chain along the axis of a linear Paul trap. Adding more ions (a few tens or hundreds) gives rise to Coulomb crystals. We created an efficient simulation code which calculates the motion of such collections of ions in quasi-static radiofrequency fields of real linear quadrupole traps (including the micromotion). We include a model for laser cooling of the ions. The simulation tool can be used to study the formation and the dynamics of Coulomb crystals under conditions corresponding to various experimental setups.
This thesis describes experimental work performed on laser cooled magnesium ions, confined in a quadrupole ion trap operating in the Penning or the combined mode. Information is gained about the dynamical motion of the ions. This is done by analyzing the time delays between scattered fluorescence photons in the case of small ion clouds (generally less than ten ions). For larger clouds (upwards of 100 ions), a fraction of the ions is "tagged" and a subsequent study made of the time evolution of the fluorescence. We have developed an innovative, non-invasive method for measuring ion oscillation frequencies which is based on analyzing photon-photon correlations present in the emitted ion fluorescence. This technique has been used to measure all three Penning trap frequencies for a wide range of dc voltage. The data have been fitted to theory and we have obtained a global fit of these data to one set of trap parameters. We also demonstrate that our technique enables us to measure space-charge shifted values of the trap resonances. This method has also been applied to the combined trap and we report experimental verification of the predicted trap resonances for a wide range of trapping parameters. These data fit well to theory. This is for all three oscillation frequencies for one set of trap parameters consistent with the data for the Penning trap. \nFurther experiments are reported concerned with the dynamics of larger ion clouds in a Penning trap. A pulsed laser is used to "tag" a small number of the ions in large ion clouds. This removes those ions from the cooling cycle by placing them in a metastable state. Subsequently, we have monitored the time evolution of the fluorescence. By analyzing these data we have been able to determine cloud rotation frequencies for large ensembles of ions.
We study the general aspects of the dynamics of an ion trapped in an ideal multipolar radio-frequency trap while interacting with a dense cold atomic gas. In particular, we explore the dynamical stability, the energy relaxation, and the characteristic harmonic motion exhibited by a trapped Yb+{\mathrm{Yb}}^{+}Yb+ ion in different multipolar potentials and immersed in various cold atomic samples (Li, Na, Rb, Yb). For this purpose, we use two different molecular-dynamics simulations, one based on a time-event drive algorithm and the other based on the stochastic Langevin equation. Relevant values for experimental realizations, such as the associated ion's lifetimes and observable distributions, are presented along with some analytical expressions that relate the ion's dynamical properties with the trap parameters.
Trapped singly charged ions can crystallize as a result of laser cooling. The emerging structure depends on the number of particles and on the geometry of the trapping potential. In linear multipole radio frequency traps, the geometry of the radial potential can lead to the formation of single-ring structures. We analyze the conditions and stability of single rings as a function of the number of poles. The rings form tubes for a large number of ions and sufficiently small trap aspect ratios. In these structures the arrangement of the ions corresponds to a triangular lattice folded onto a cylinder. The stability of the tubular structures is numerically studied for different lattice constants and their normal-mode spectrum is determined.