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arXiv:1807.10500 · Review of Scientific Instruments

Correcting symmetry imperfections in linear multipole traps

J. Pedregosa-Gutierrez, C. Champenois, M. Houssin, Marius Romuald Kamsap, Martina Knoop

Published Dec 1, 2018• 7 citations
arXivHTMLPDF

Abstract

Multipole radio-frequency (RF) traps are central to collisional experiments in cryogenic environments. They also offer possibilities to generate new type of ion crystals topologies and in particular the potential to create infinite 1D/2D structures: ion rings and ion tubes. However, multipole traps have also been shown to be very sensitive to geometrical misalignment of the trap rods, leading to additional local trapping minima. The present work proposes a method to correct non-ideal potentials, by modifying the applied RF amplitudes for each trap rod. This approach is discussed for the octupole trap, leading to the restitution of the ideal Mexican-Hat-like pseudo-potential, expected in multipole traps. The goodness of the compensation method is quantified in terms of the choice of the diagnosis area, the residual trapping potential variations, the required adaptation of the applied RF voltage amplitudes, and the impact on the trapped ion structures. Experimental implementation for macroscopic multipole traps is also discussed, in order to propose a diagnostic method with respect to the resolution and stability of the trap drive. Using the proposed compensation technique, we discuss the feasibility of generating a homogeneous ion ring crystal, which is a measure of quality for the obtained potential well.

DOI
10.1063/1.5075496

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Multipole radio-frequency (RF) traps are central to collisional experiments in cryogenic environments. They also offer possibilities to generate new type of ion crystals topologies and in particular the potential to create infinite 1D/2D structures: ion rings and ion tubes. However, multipole traps have also been shown to be very sensitive to geometrical misalignment of the trap rods, leading to additional local trapping minima. The present work proposes a method to correct non-ideal potentials, by modifying the applied RF amplitudes for each trap rod. This approach is discussed for the octupole trap, leading to the restitution of the ideal Mexican-Hat-like pseudo-potential, expected in multipole traps. The goodness of the compensation method is quantified in terms of the choice of the diagnosis area, the residual trapping potential variations, the required adaptation of the applied RF voltage amplitudes, and the impact on the trapped ion structures. Experimental implementation for macroscopic multipole traps is also discussed, in order to propose a diagnostic method with respect to the resolution and stability of the trap drive. Using the proposed compensation technique, we discuss the feasibility of generating a homogeneous ion ring crystal, which is a measure of quality for the obtained potential well.
Abstract Radio-frequency (RF) linear multipole traps have been shown to be very sensitive to mis-positioning of their electrodes, which results in a symmetry breaking and leads to extra local minima in the trapping potential as shown in Pedregosa-Gutierrez et al (2018 J. Mod. Opt. 65 529) disturbing the operation of the trap. In this work, we analytically describe the RF-potential of a realistic octupole trap by including lower order terms to the well-established equation for a perfectly symmetric octupole trap. We describe the geometry by a combination of identified defects, characterized by simple analytical expressions. A complete equation is proposed for a trap with any electrode deviation relying on a combination of the simple cases where the defects are taken individually. Our approach is validated by comparison between analytical and numerical results for defect sizes up to 4% of the trap radius. As described in Pedregosa-Gutierrez et al (2018 Rev. Sci. Instrum. 89 123101), an independent fine-tuning of the amplitude of the RF voltage applied on each electrode can be used to mitigate the geometrical defects of a realistic trap. In a different way than in Pedregosa-Gutierrez et al (2018 Rev. Sci. Instrum. 89 123101), the knowledge of an analytical equation for the potential allows to design the set of RF-voltages required for this compensation, based on the experimental measurement of the ion positions in the trap, without information concerning the exact position of each electrode, and with a small number of iterations. The requirements, performances and limitations of this protocol are discussed via comparison of numerical simulations and analytical results.
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.
Radiofrequency multipole traps have been used for some decades in cold collision experiments and are gaining interest for precision spectroscopy due to their low micromotion contribution and the predicted unusual cold-ion structures. However, the experimental realisation is not yet fully controlled, and open questions in the operation of these devices remain. We present experimental observations of symmetry breaking of the trapping potential in a macroscopic octupole trap with laser-cooled ions. Numerical simulations have been performed in order to explain the appearance of additional local potential minima and be able to control them in a next step. We characterise these additional potential minima, in particular with respect to their position, their potential depth and their probability of population as a function of the radial and angular displacement of the trapping rods.
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.
Ion Coulomb crystals of laser-cooled Ca+{\text{Ca}}^{+}Ca+ ions have been observed in a cryogenic linear octupole rf ion trap for the first time. Due to the almost field-free central region, large ion crystals containing over 104{10}^{4}104 ions of millimeter size were successfully produced. The shapes of the crystals can be manipulated by changing the static voltages applied to the octupole rods and the endcap electrodes. Quasi-two-dimensional Coulomb crystals consisting of a small number of ions were also observed with single-ion sensitivity. When a large number of ions is crystallized in the octupole trap, a new kind crystal image with a dip along the axial direction was obtained. The results show that a linear octupole trap and multipole traps are available for producing large, cold, and novel ion Coulomb crystals. The planar ring-type crystal which has not been observed before may lead to future interesting applications.
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.