Optical Clocks with Trapped Ions: Atomic and Nuclear Clocks

Peik, Ekkehard

doi:10.1364/cleo_si.2022.stu5o.5

Cited by 2 publications

(2 citation statements)

References 4 publications

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“…Besides, ion traps also enable exceptional control in preparing and manipulating atomic quantum states [58][59][60][61][62][63], which is why their wide area of applications also includes quantum logic [64][65][66][67][68], quantum sensing [69][70][71][72], quantum metrology [73,74] and even time fractals [75] or time crystals [76]. To these one adds high accuracy optical frequency standards [77][78][79][80], which are amongst the most sensitive quantum sensors [81,82] used to perform searches for physics beyond the Standard Model (BSM) [83][84][85] or to disseminate atomic time scales and redefine the SI unit of time, the second [86][87][88][89][90].…”

Section: Of 36mentioning

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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Section: Of 36mentioning

confidence: 99%

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

Mihalcea

2024

Preprint

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“…Apart from that, ITs also enable exceptional control in preparing and manipulating atomic quantum states [53][54][55][56][57][58] because they make possible applications such as quantum logic [59][60][61][62][63], quantum sensing [64][65][66][67], quantum metrology [68,69] and even time fractals [70] or time crystals [71]. To these, one adds high-accuracy optical frequency standards [72][73][74][75], which are amongst the most sensitive quantum sensors [76,77] used to perform searches for physics beyond the Standard Model (BSM) [78][79][80] or to disseminate atomic time scales and redefine the SI unit of time, the second [81][82][83][84][85]. The sensitivity of optical atomic clocks [72,86] is limited by the Standard Quantum Limit (SQL) imposed by the inherent projection noise of a quantum measurement [87].…”

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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Optical Clocks with Trapped Ions: Atomic and Nuclear Clocks

Abstract: Progress on optical clocks with laser cooled trapped ions is presented with a focus on two systems that both possess small systematic uncertainties and a high sensitivity in fundamental tests: The 171Yb+ ion with an E3 transition and the 229Th3+ ion with a low-energy nuclear transition.

Cited by 2 publications

References 4 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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