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arXiv:1103.2502 · Physical Review A

Parallel ion strings in linear multipole traps

Mathieu Marciante, C. Champenois, J. Pedregosa-Gutierrez, A. Calisti, Martina Knoop

Published Feb 18, 2011• 11 citations
arXivHTMLPDF

Abstract

Additional radio-frequency (rf) potentials applied to linear multipole traps create extra field nodes in the radial plane which allow one to confine single ions, or strings of ions, in totally rf field-free regions. The number of nodes depends on the order of the applied multipole potentials and their relative distance can be easily tuned by the amplitude variation of the applied voltages. Simulations using molecular dynamics show that strings of ions can be laser cooled down to the Doppler limit in all directions of space. Once cooled, organized systems can be moved with very limited heating, even if the cooling process is turned off.

DOI
10.1103/physreva.83.021404

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Additional radio-frequency (rf) potentials applied to linear multipole traps create extra field nodes in the radial plane which allow one to confine single ions, or strings of ions, in totally rf field-free regions. The number of nodes depends on the order of the applied multipole potentials and their relative distance can be easily tuned by the amplitude variation of the applied voltages. Simulations using molecular dynamics show that strings of ions can be laser cooled down to the Doppler limit in all directions of space. Once cooled, organized systems can be moved with very limited heating, even if the cooling process is turned off.
We report a linear surface-electrode trap that can be used to form parallel ion strings. By adjusting the balance of the radio-frequency (RF) voltages applied to central and RF electrodes, the RF pseudopotential can be varied from single-well to double-well in the radial direction. Ions located on two parallel lines of the RF potential null are in principle free from excess micromotion if appropriate static voltages are applied. Calcium ions were trapped for the evaluation of the designed electrode. An ion string in the single-well potential and two ion strings in the double-well potential were observed by changing the RF voltages. Such traps could be used for quantum simulation of coupled spin systems.
We analyze the possibility of cooling ions with a single laser beam, due to the coupling between the three components of their motion induced by the Coulomb interaction. For this purpose, we numerically study the dynamics of ion clouds of up to 140 particles, trapped in a linear quadrupole potential and cooled with a laser beam propagating in the radial plane. We use molecular dynamics simulations and model the laser cooling by a stochastic process. For each component of the motion, we systematically study the dependence of the temperature on the anisotropy of the trapping potential. Results obtained using the full radio-frequency (rf) potential are compared to those of the corresponding pseudopotential. In the rf case, the rotation symmetry of the potential has to be broken to keep ions inside the trap. Then, as for the pseudopotential case, we show that the efficiency of the Coulomb coupling to thermalize the components of motion depends on the geometrical configuration of the cloud. Coulomb coupling appears to be not efficient when the ions organize as a line or a pancake and the three components of motion reach the same temperature only if the cloud extends in three dimensions.
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.
The nonlinear dynamics of large ion clouds ($N\ensuremath{\ge}256$ ions) trapped in radio-frequency (rf) traps and coupled to laser cooling give rise to a bistable behavior of the temperature. Numerical simulations of the free evolution of a large three-dimensional spherical cloud is used to characterize how the oscillating field amplitude and the ion number control the rf-heating rate and the switching between the two stable states. We show that the heating rate does not significantly depend on the ion number but strongly depends on the oscillating field. This exhibits the major role played by the density of the ensemble. The competition between the radio-frequency heating and the laser cooling is also discussed. They are used to design scenarios to take advantage of the threshold effect to detect and quantify perturbations by an intruder.
A laser-cooling experiment with Ca+{\mathrm{Ca}}^{+}Ca+ ions trapped in a linear rf octupole ion trap is presented. The phase transition of the laser-cooled Ca+{\mathrm{Ca}}^{+}Ca+ ions from the cloud to the crystal state is observed by an abrupt dip of the laser-induced fluorescence spectrum and indicates that mK temperatures are obtained. We have also performed molecular dynamics simulations under various conditions to confirm this property by deducing axially symmetric structures of Coulomb crystals and by evaluating the translational temperatures of the laser-cooled ions. The simulation results show that for small numbers of ions novel ring-shaped crystals are produced. As the number of ions is increased, cylindrical layers in the ring crystal are sequentially formed. For more than 100 ions, also hexagonal and spiral structures emerge in parts of the large-size ion crystal, which has a length on the order of millimeters for the present geometrical arrangement and voltages. An advantage of the linear rf octupole trap is its large almost-field-free region in the middle of the trap, where the micromotion amplitude is small for trapped ions. These results demonstrate that such a multipole trap has attractive features for quantum computing and ultracold ion-atom collision studies.
This paper reviews the basic principles of ion storage and cooling in the first place, and presents simulation result using a molecular dynamics method on ion distribution and RF heating rate. Based on this result, we evaluate the influence of RF heating effect and micromotions of the ions on frequency standards. Compared to conventional quadrupole trap, a 12-pole trap is able to reduce the RF heating rate of the ion cloud and to enable narrowing the linewidth with the Ramsey method. Moreover, the effective potential in the 12-pole trap has a flat bottom and a steep wall, which is capable of reducing the second order Doppler effect caused by the micromotions and thus helpful to enhance the accuracy and stability of the clock. At last, we review previous work of JPL on high performance, 199Hg+ ion clocks and our present work of laser-cooled, 113Cd+ ion clock based on the multipole trap.