Electrostatic anharmonicity in cylindrical Penning traps induced by radial holes to the trap center

Chimwal, Deepak; Kumar, Sugam; Joshi, Yash; Lal, Aditya Aryan; Nair, Lekha; Quint, Wolfgang; Vogel, Manuel

doi:10.1088/1402-4896/ad38e7

Cited by 2 publications

(2 citation statements)

References 43 publications

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“…Different ion trap geometries and electrode space arrangements are generally used (especially hyperbolic and cylindrical traps) in order to achieve a harmonic (electric) trapping potential around the trap center. Whilst hyperbolic geometries surround the trap center almost entirely, cylindrical ones usually exhibit open-endcap designs that allow better axial access to the center and enhanced interaction between levitated particles and laser beams used for cooling or manipulation [171], which makes them suited for MS, quantum optics, optical frequency metrology and quantum information processing (QIP) applications. For this reason, classical (hyperbolic) endcap electrode geometries are frequently employed when building single-ion optical clocks, as they provide certain benefits such as a saddle-shaped trapping potential which is essentially quadrupole, along with an open electrode structure that enables effective fluorescence detection [90,105].…”

Section: Discussionmentioning

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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Section: Discussionmentioning

confidence: 99%

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

Mihalcea

2024

Photonics

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“…Different ion trap geometries and electrode space arrangements are generally used (especially hyperbolic and cylindrical traps), in order to achieve a harmonic (electric) trapping potential around the trap centre. Whilst hyperbolic geometries surround the trap centre almost entirely, cylindrical ones usually exhibit open-endcap designs that allow better axial access to the centre and enhanced interaction between levitated particles and laser beams used for cooling or manipulation [140], which makes them suited for quantum logic, quantum optics and quantum metrology applications. For this reason, classical (hyperbolic) endcap electrode geometries are frequently employed when building single ion optical clocks, as they provide certain benefits such as a saddle shaped trapping potential which is essentially quadrupole, along with an open electrode structure that enables effective fluorescence detection [104,106].…”

Section: Ultraprecise Optical Atomic Clocks Based On Ultracold Ions C...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 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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Electrostatic anharmonicity in cylindrical Penning traps induced by radial holes to the trap center

Cited by 2 publications

References 43 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

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