Nano- and microparticle Nonlinear Damping Identification in quadrupole trap

Rybin, Vadim; Rudyi, Semyon; Rozhdestvensky, Yu.

doi:10.1016/j.ijnonlinmec.2022.104227

Cited by 9 publications

(6 citation statements)

References 54 publications

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“…To complicate the picture even more, the ion also undergoes interaction with a laser field [126], in presence of contributions from the hexapole and octopole fields that superpose over the harmonic trap potential. Hence, it was demonstrated that a damped parametric oscillator (PO) levitated in a Paul trap exhibits fractal properties and complex chaotic orbits, along with the emergence of strange attractors (which are often called fractal sets) [126,127]. Ion motion on the strange attractor exhibits sensible dependence on the initial conditions.…”

Section: Of 36mentioning

confidence: 99%

“…[126] reports on the dynamics of an ion confined in a nonlinear Paul trap [61,122,176], assimilated with a time-periodic differential dynamical system. As such systems are characterized by low dissipation, exotic phenomena can be observed such as strange attractors, limit cycles, period doubling bifurcation and fractal basin boundaries [75,127,175]. We investigate the following equation of motion, which describes the axial dynamics for a particle of mass M and electric charge Q, confined within a quadrupole Paul trap, with anharmonicity derived from an octopole (quartic) electric potential λz 4 /4 [126,177]:…”

Section: Anharmonic Corrections For Electrodynamic (Paul) Traps Pertu...mentioning

confidence: 99%

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Mathieu-Hill Equation Stability Analysis for Trapped Ions. Anharmonic Corrections for Nonlinear Electrodynamic Traps

Mihalcea

2024

Preprint

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The stability properties of the Hill equation are discussed, and especially those of the Mathieu equation that characterize ion motion in electrodynamic traps. The solutions of the Mathieu equation for a trapped ion are characterized by using the Floquet theory and Hill's Method solution, which yields an infinite system of linear and homogeneous equations whose coefficients are recursively determined. Stability is discussed for parameters $a$ and $q$ that are real. Characteristic curves are introduced naturally by the Sturm-Liouville problem for the well known even and odd Mathieu equations $ce_m(z,q)$ and $se_m(z,q)$. We illustrate the stability diagram for a combined (Paul and Penning) trap and represent the frontiers of the stability domains for axial and radial motion. In case of a Paul trap the stable solution corresponds to a superposition of harmonic motions. The problem of evaluating the maximum amplitudes of stable oscillations for the ideal conditions (taken into consideration) is also approached. Anharmonic corrections are discussed within the frame of the perturbation theory, while the frontiers of the modified stability domains are determined as a function of the chosen perturbation parameter. The results apply to 2D and 3D ion traps used for different applications in quantum engineering, among which optical clocks, quantum logic and quantum metrology, but not restricted only to these.

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Section: Of 36mentioning

confidence: 99%

Section: Anharmonic Corrections For Electrodynamic (Paul) Traps Pertu...mentioning

confidence: 99%

Mathieu-Hill Equation Stability Analysis for Trapped Ions. Anharmonic Corrections for Nonlinear Electrodynamic Traps

Mihalcea

2024

Preprint

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“…The stability diagram for an electrodynamic (Paul) trap is illustrated as a function of the Mathieu function eigenvalues. We also illustrate the stability diagram for a combined trap, where both axial and radial dynamics are considered, and we investigate the damped PO which generally exhibits fractal properties, chaotic complex orbits and exotic attractors [125,126,133]. Ion trajectories in the phase space are explored and we infer the transfer matrix along with the maximum amplitude of stable oscillations for ions confined in a quadrupole Paul trap.…”

Section: Structure Of the Papermentioning

confidence: 99%

“…To complicate the picture even more, the ion also undergoes interaction with a laser field [125], in presence of contributions from the hexapole and octopole fields that superpose over the harmonic trap potential. Hence, it was demonstrated that a damped parametric oscillator (PO) levitated in a Paul trap exhibits fractal properties and complex chaotic orbits, along with the emergence of strange attractors (which are often called fractal sets) [125,126]. Ion motion on the strange attractor exhibits sensible dependence on the initial conditions.…”

Section: Introductionmentioning

confidence: 99%

Mathieu–Hill Equation Stability Analysis for Trapped Ions: Anharmonic Corrections for Nonlinear Electrodynamic Traps

Mihalcea

2024

Photonics

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The stability properties of the Hill equation are discussed, especially those of the Mathieu equation that characterize ion motion in electrodynamic traps. The solutions of the Mathieu-Hill equation for a trapped ion are characterized by employing the Floquet theory and Hill’s method solution, which yields an infinite system of linear and homogeneous equations whose coefficients are recursively determined. Stability is discussed for parameters a and q that are real. Characteristic curves are introduced naturally by the Sturm–Liouville problem for the well-known even and odd Mathieu equations cem(z,q) and sem(z,q). In the case of a Paul trap, the stable solution corresponds to a superposition of harmonic motions. The maximum amplitude of stable oscillations for ideal conditions (taken into consideration) is derived. We illustrate the stability diagram for a combined (Paul and Penning) trap and represent the frontiers of the stability domains for both axial and radial motion, where the former is described by the canonical Mathieu equation. Anharmonic corrections for nonlinear Paul traps are discussed within the frame of perturbation theory, while the frontiers of the modified stability domains are determined as a function of the chosen perturbation parameter and we demonstrate they are shifted towards negative values of the a parameter. The applications of the results include but are not restricted to 2D and 3D ion traps used for different applications such as mass spectrometry (including nanoparticles), high resolution atomic spectroscopy and quantum engineering applications, among which we mention optical atomic clocks and quantum frequency metrology.

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“…4 RF traps support a wide range of methods and techniques to measure physical properties of a trapped particle, such as mass, size, density, and surface charge. [5][6][7] Development of optical spectral analysis approaches with RF traps gives a new insight to single particle comprehensive study.…”

Section: Introductionmentioning

confidence: 99%

Photoluminescence of quantum dot cluster in quadrupole Paul trap

Rybin¹,

Shcherbinin²,

Rudyi³

et al. 2023

SPIE Future Sensing Technologies 2023

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Nowadays nanostructures are in demand in various fields from biomedicine to green energy. Photoluminescence (PL) spectral measurements are a powerful tool to study nanomaterials unique physical and optical properties. Most modern spectral approaches are associated with the study of a sample on a substrate or in colloidal solution.In turn, we propose a technique for studying the luminescence of a single object levitating in a quadrupole Paul trap. To verify the technique, we investigate PL spectra of individual trapped charged microcluster of CdSe/ZnS quantum dots. The results obtained open prospects of optical research on single particles isolated from the environment.

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Nano- and microparticle Nonlinear Damping Identification in quadrupole trap

Cited by 9 publications

References 54 publications

Mathieu-Hill Equation Stability Analysis for Trapped Ions. Anharmonic Corrections for Nonlinear Electrodynamic Traps

Mathieu-Hill Equation Stability Analysis for Trapped Ions. Anharmonic Corrections for Nonlinear Electrodynamic Traps

Mathieu–Hill Equation Stability Analysis for Trapped Ions: Anharmonic Corrections for Nonlinear Electrodynamic Traps

Photoluminescence of quantum dot cluster in quadrupole Paul trap

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