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Coupled-oscillator model to analyze the interaction between a quartz resonator and trapped ions

E. Altozano, J. Berrocal, S. Lohse, F. Domínguez, M. Block, J. J. García-Ripoll, and D. Rodríguez
Phys. Rev. A 107, 053116 – Published 30 May 2023
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Article Text
  • INTRODUCTION
  • PENNING TRAP AND INDUCED IMAGE CURRENT
  • THE QUARTZ-ION COUPLED-OSCILLATOR MODEL
  • EXPERIMENTAL SIGNAL COMPUTATION
  • RESULTS AND DISCUSSION
  • CONCLUSIONS AND OUTLOOK
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    The novel application of a piezoelectric quartz resonator for the detection of trapped ions has enabled the observation of the quartz-ions interaction under nonequilibrium conditions, opening new perspectives for high-sensitive motional frequency measurements of radioactive particles. Energized quartz crystals have (long) decay-time constants in the order of milliseconds, permitting the coherent detection of charged particles within short time scales. In this paper we develop a detailed model governing the interaction between trapped Ca+40 ions and a quartz resonator connected to a low-noise amplifier. We apply this model to experimental data and extract the ions' reduced-cyclotron frequency in our 7-T Penning trap setup. We also obtain an upper limit for the coupling constant g with the present quartz-amplifier-trap (QAT) configuration. The study of the reduced-cyclotron frequency is especially important for the use of this resonator in precision Penning-trap mass spectrometry. The improvement in sensitivity can be accomplished by increasing the quality factor of the QAT configuration, which in turn will improve the performance of the system towards the strong-coupling regime.

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    • Received 11 July 2022
    • Accepted 9 May 2023

    DOI:https://doi.org/10.1103/PhysRevA.107.053116

    ©2023 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Quantum coherence & coherence measures
    1. Physical Systems
    Trapped ions
    1. Techniques
    Cyclotron resonancePenning traps
    Atomic, Molecular & Optical

    Authors & Affiliations

    E. Altozano1, J. Berrocal1, S. Lohse2,3,4, F. Domínguez1, M. Block2,3,4, J. J. García-Ripoll5, and D. Rodríguez1,6,*

    • 1Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071 Granada, Spain
    • 2Department Chemie, Standort TRIGA, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany
    • 3GSI Helmholtzzentrum für Schwerionenforschung GmbH, D-64291 Darmstadt, Germany
    • 4Helmholtz-Institut Mainz, D-55099 Mainz, Germany
    • 5Instituto de Física Fundamental, IFF-CSIC, Serrano 113, 28006 Madrid, Spain
    • 6Centro de Investigación en Tecnologías de la Información y las Comunicaciones, Universidad de Granada, 18071 Granada, Spain

    • *danielrodriguez@ugr.es

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    Issue

    Vol. 107, Iss. 5 — May 2023

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    Images

    • Figure 1
      Figure 1

      Transverse cut of a ring electrode in a Penning trap with cylindrical symmetry. The electrode is divided in four segments. The ions' trajectory in the radial plane, considering only modified-cyclotron motion for illustration purposes, is depicted by the blue-solid line. The light and dark-gray solid circles represent the trapped ions when they are far or close, respectively, to the detection segment (DS) where the current they induce is picked up. DS is connected to the quartz resonator followed by an amplifier [8].

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    • Figure 2
      Figure 2

      Schematic view of the quartz-ion coupled-oscillators model. The external (rf) voltage is applied to the electrode on the left.

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    • Figure 3
      Figure 3

      Left panel: nqV02 (top) and Snoise (bottom) as a function of the time t0. Right panel: FWHM≡γq/2π as a function of the time t0.

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    • Figure 4
      Figure 4

      PSD signal as a function of the frequency for t0=0 ms. A zoomed plot is shown in the right panel. The red-solid line in both panels (fit 1) is the S(ω) fit. The blue-dashed-dotted line (fit 2) is the Sth(ω)+Snoise fit. χν2=1.18. The data points and standard deviations (1 σ) are the results from N=20 measurements.

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    • Figure 5
      Figure 5

      Evolution of the PSD signal and fitting function for different times t0. The data points and standard deviations are the results from N=20 measurements.

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    • Figure 6
      Figure 6

      Evolution of νion obtained from the fit using Eq. (29) as a function of t0. The vertical line covers 50 mHz.

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    • Figure 7
      Figure 7

      PSD signals as a function of the frequency for t0=5 ms (top) and t0=14 ms (bottom). The red-solid line (fit 1) is the S(ω) fit. The Sth(ω) fit is not shown since it is not visible in this scale. Note that the PSD is two orders of magnitude larger compared to Fig. 4 because the rf field amplitude applied here is 16 times larger. The data points and standard deviations are the results from three measurements.

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    • Figure 8
      Figure 8

      S(ω,t0) for a fixed frequency ω1.

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    • Figure 9
      Figure 9

      Time evolution of |〈a(t0)〉| and |〈b(t0)〉|.

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