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Journal of Modern Optics

Characteristics of Trapped Ions in the Second Stability Region of a Paul Trap

Xiwen Zhu, Dongxiang Qi

Published Feb 1, 1992• 12 citations
Publisher

Abstract

Characteristics of single ion motion and mechanisms of trapping ions in the second stability region of a Paul trap are discussed. The mean kinetic energy and mean width of the spatial distribution of an ion cloud in that region are calculated. Similarities and differences of the results between the first and second stability regions are emphasized.

DOI
10.1080/09500349214550291

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Characteristics of single ion motion and mechanisms of trapping ions in the second stability region of a Paul trap are discussed. The mean kinetic energy and mean width of the spatial distribution of an ion cloud in that region are calculated. Similarities and differences of the results between the first and second stability regions are emphasized.
The stability regions of an ion in a two-dimensional Paul trap are studied by a quantum-mechanical treatment, which is very important for the experiment when the temperature is fairly low. The result is compared with a classical one published before by Paul [Rev. Mod. Phys. 62, 531 (1990)]. It is shown that their properties are quite similar and their differences are related to the quantum effect, which cannot be included within a classical description. All of these properties are discussed in detail.
Confinement of ion clouds in an rf octupole ion trap is investigated with particular emphasis on the trapping stability, which is position dependent. Excitation spectra of trapped clouds of Ba+{\mathrm{Ba}}^{+}Ba+ ions are observed, and the kinetic energy of ion clouds is derived. The spatial extension of ion clouds is measured, providing the basis for an experimental study of the trapping stability. For ion clouds in an rf octupole trap the mean kinetic energy is smaller and the spatial extension is larger than in comparable Paul traps.
In this paper, we present and discuss stability diagrams for Paul traps driven by two ac voltages. In contrast to a typical Paul trap, here we suggest a secondary ac voltage whose frequency is twice the frequency of the primary one. The ratio between their amplitudes can be used to expand the region of stability and to access different states of motion of trapped ions. This provides a further mechanism to trap, cool, and manipulate single ions and also to improve the experimental framework where ion clouds and crystals can be prepared and controlled. Such approach opens the possibility of designing more sophisticated trapping architectures, leading to a wide variety of applications on ion trap research and mass analysis techniques.
Motivated by recent developments in ion trap design and fabrication, we investigate the stability of the motion of an ion in asymmetrical, planar versions of the linear Paul trap. The equations of motion of an ion in such a trap are generally coupled due to a nonzero relative angle θ between the principal axes of RF and DC fields, invalidating the assumptions behind the standard stability analysis for symmetric Paul traps. Using numerical methods, we obtain stability diagrams for the coupled system for various values of θ, generalizing the standard q-a stability diagrams. We then use multi-scale perturbation theory to obtain approximate formulas for the boundaries of the primary stability region and check our formulas against results from numerical analysis. Our results show that while the primary stability region is quite robust to changes in θ, a secondary stability region is highly variable, joining the primary stability region at the special case of θ=45°, which results in a significantly enlarged stability region for this particular angle. We conclude that while the standard stability diagrams for classical, symmetric Paul traps are not entirely accurate for asymmetric surface traps (or for other types of traps with a relative angle between the RF and DC axes), they are “safe” in the sense that operating conditions deemed stable according to standard stability plots are in fact stable for asymmetric traps, as well. By ignoring the coupling in the equations, one only underestimates the size of the primary stability region.
We study the quantum stability of the dynamics of ions in a Paul trap. We revisit previous results that showed that quantum trajectories did not have the same region of stability as their classical counterpart, contrary to what is obtained from a Floquet analysis of the motion in the periodic trapping field. Using numerical simulations of the full wave-packet dynamics, we confirm that the classical trapping criterion is fully applicable to quantum motion, when considering both the expectation value of the position of the wave packet and its width.