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Europhysics Letters (EPL)

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

J. Walz, Ingo Siemers, Michael Schubert, Werner Neuhauser, R. Blatt

Published Jan 10, 1993• 10 citations
Publisher

Abstract

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.

DOI
10.1209/0295-5075/21/2/011

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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.
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.
The stability properties of radio-frequency traps make them a technology of choice for the design of embedded microwave ion clocks for deep space navigation applications. The main effect limiting the frequency stability of such clocks is the frequency shift induced by the second order Doppler effect which fluctuates with the number of trapped ions. The use of radio-frequency multipole traps in the design of microwave clocks is motivated by a built-in reduction of the radio-frequency driven motion of the ions with the increase of the order of the multipole field. Experimental realizations by NASA-JPL of ion clocks involving higher order multipole traps have demonstrated a stability gain, but no direct measurement has yet been undertaken to clarify wherever this gain is a direct consequence of the number of electrodes in the trap or from a global optimization of the whole setup. One of the objectives of the TADOTI experiment is to conduct a comparative measurement of the velocity distribution over a laser cooled Ca+ ion cloud trapped in a quadrupole and an octupole trap. Observations of cold samples have shown an inhomogeneous spatial distribution of the trapped particles with clustering of the ions in local potential wells. Simulations attribute this organization to a symmetry breaking in the trap, induced by realistic mis-positioning of the electrodes. A prerequisite for the velocity distribution characterization is to restore to symmetry of the potential of the octupole trap by tuning the RF voltage applied to each electrode. This thesis focuses on the analytical description of the potential perturbations induced by the structural deformation of the trap, and proposes a characterization and compensation protocol of the perturbations, based on the localization of the laser-cooled ion in the trap. These tools can be used to create any configuration of three parallel ion clouds in the octupole trap.
The stability of a linear ac trap for neutral polar molecules is investigated both theoretically and experimentally. While the overall stability is found to be well described by the linearized equations of motion within the usual framework of stability diagrams, instabilities similar to those observed in anharmonic radio-frequency ion traps occur inside the nominal stable regions. These motional resonances are caused by strong anharmonic contributions to the trapping fields, that inevitably appear in ac traps for polar molecules. Nonlinear resonant energy transfer from the high-frequency source to molecules inside the trap is observed for the particles' fundamental frequency of transverse oscillation being 14\frac{1}{4}41​ of the forcing frequency.
We consider the stability of systems subjected to periodic parametric driving such that their equations of motion are ordinary differential equations with periodic coefficients and carry out a detailed analysis of important aspects of such systems in the context of the confinement of ions by oscillating electric fields. We show how they can be understood in terms of a pseudopotential approximation and resonances arising from the parametric excitation and investigate the properties of a novel linear Paul trap configuration operating with two radio-frequencies to simultaneously confine two species with extremely different charge-to-mass ratios. The theoretical calculations have been verified by molecular dynamics simulations and normal modes analysis.
When ions of slightly different mass and the same charge are stored in a radio-frequency electric quadrupole trap, a collective oscillation is observed rather than the independent motions usually assumed. A high-temperature model of ion clouds, each characterized by ions of one mass, shows that the ions of each cloud move as a unit and exhibit a correlated motion with the other clouds when a strong coupling condition is satisfied. This phenomenon is expected to arise whenever more than one ion is trapped and might be observable in neutral atom traps as well.
We investigate the quantum dynamics of a single ion confined in a radio-frequency (RF) Paul trap in the presence of weak octupole-induced anharmonicity, as can occur in realistic ion-trap potential. The explicitly time-dependent quadrupole potential is treated in a reference-oscillator Fock basis, allowing the effects of the RF drive and the quartic correction to be resolved directly at the level of motional-state couplings. While the quadratic RF interaction generates Δn=±2Δn=\pm2Δn=±2 transitions and Gaussian squeezing, the quartic contribution opens additional Δn=±4Δn=\pm4Δn=±4 coupling pathways. Starting from the reference-oscillator vacuum, we show that the octupole interaction broadens the even-parity Fock-state distribution and enhances the phonon-number fluctuations more strongly than the mean occupation. At the same time, the RF-induced sub-vacuum quadrature squeezing remains robust, although its magnitude and orientation are modified by the quartic interaction. The number statistics and quadrature fluctuations therefore respond differently to the same nonlinear perturbation, reflecting the distinct roles of Fock-space redistribution and phase coherence. The resulting dynamics provide a quantum-mechanical characterization of weak octupole corrections beyond the ideal quadrupole approximation and clarify how realistic anharmonicities modify nonclassical trapped-ion motion. Importantly, the motional nonclassicality remains robust against the weak octupole perturbation, as evidenced by persistent sub-vacuum quadrature squeezing and Klyshko-inequality violation. These results characterize how realistic anharmonic corrections reshape trapped-ion motion beyond the ideal quadrupole approximation.