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Design optimization and precision requirements of an endcap ion trap for single-ion optical clock applications

Chaowei Wang, Shaoyang Dai, Yani Zuo, Fang Fang

Published May 1, 2025• 2 citations

Abstract

Ion traps serve as the venue for confining ions and exciting ionic transitions in ion optical clocks, where the geometric dimensions of the electrodes within the ion trap directly impact the performance metrics of the ion optical clocks. In this study, the finite element analysis method was employed to simulate the relationship between the electric field distribution and the dimensions of the electrodes in an endcap ion trap. The simulation data were subjected to curve fitting, with trap depth and potential anharmonicity utilized as the primary evaluation criteria for optimizing ion trap design. The results indicate that the ion trap demonstrates optimal performance when the distance between the radio frequency electrodes is reduced to 0.686 mm, and it is suggested that the chamfer width of the endcap electrode extension be 0.6 mm. Based on this, the study further explored the machining accuracy of certain dimensions, concluding that the required high machining accuracy values for the radio frequency electrodes and the endcap electrodes are ±3 and ±7 μm, respectively, while the aperture machining accuracy requirements are ±3 and ±22 μm, respectively. In addition, the simulation results suggest that a conical surface on the radio frequency electrodes with a height of ∼0.08 mm aids in reducing anharmonicity, although a spherical end surface does not notably improve the electric field distribution. These findings provide a valuable reference for the optimized design and machining of ion traps.

DOI: 10.1063/5.0271817

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Ion traps serve as the venue for confining ions and exciting ionic transitions in ion optical clocks, where the geometric dimensions of the electrodes within the ion trap directly impact the performance metrics of the ion optical clocks. In this study, the finite element analysis method was employed to simulate the relationship between the electric field distribution and the dimensions of the electrodes in an endcap ion trap. The simulation data were subjected to curve fitting, with trap depth and potential anharmonicity utilized as the primary evaluation criteria for optimizing ion trap design. The results indicate that the ion trap demonstrates optimal performance when the distance between the radio frequency electrodes is reduced to 0.686 mm, and it is suggested that the chamfer width of the endcap electrode extension be 0.6 mm. Based on this, the study further explored the machining accuracy of certain dimensions, concluding that the required high machining accuracy values for the radio frequency electrodes and the endcap electrodes are ±3 and ±7 μm, respectively, while the aperture machining accuracy requirements are ±3 and ±22 μm, respectively. In addition, the simulation results suggest that a conical surface on the radio frequency electrodes with a height of ∼0.08 mm aids in reducing anharmonicity, although a spherical end surface does not notably improve the electric field distribution. These findings provide a valuable reference for the optimized design and machining of ion traps.

With the decrease in dimension of ion traps employed in optical frequency standards and precision spectroscopy, the sensitivity of trapping behavior to trap geometry is more and more prominent. We present a guide for the design and construction of a miniature trap for a single ion confinement, and propose an optimized combination of r ring /r endcap ≈ 0.5 and z 0 ≈ r 0 within the range of r 0 = 0.7 ± 0.2 mm. Compared with the trap used by Huang et al. [ Phys. Rev. A 84 (2011) 053841 ], the design can lead to an increase in trap pseudo-potential of more than 20% and a reduction on potential anharmonicity of more than 90%. The improvements make the trap closer to an ideal hyperboloidal trap to confine a single ion tightly with the benefit of weaker micro-motion. Considering the imperfection of electrodes machining and traps alignment, we also demonstrate the importance of trap symmetry, especially on two endcap electrodes.

As part of the ongoing world-wide effort in improving time and frequency references, a high accuracy optical frequency standard was developed using the electric quadrupole allowed clock transition at 445 THz (674 nm) in a trapped and laser cooled 88Sr+ion. An ion trap system of the endcap design has been recently evaluated with a fractional frequency uncertainty which surpasses the accuracy of the current realization of the SI second. This thesis seeks to further evaluate the limiting systematic shifts of the device by optimizing a second ion trap reference based on a rf Paul trap design, which was then compared with the endcap trap reference frequency. The comparison of the two ion traps' reference frequencies confirmed an overall offset of -0.36 pm 0.08 Hz at the 445 THz reference frequency corresponding to a fractional frequency offset of 8 x 10^-16.

Ion traps can provide both physical implementation of quantum information processing and direct observation of quantum systems. Recently, surface ion traps have been developed using microfabrication technologies and are considered to be a promising platform for scalable quantum devices. This paper presents detailed guidelines for designing the electrodes of surface ion traps. First, we define and explain the key specifications including trap depth, q-parameter, secular frequency, and ion height. Then, we present a numerical-simulation-based design procedure, which involves determining the basic assumptions, determining the shape and size of the chip, designing the dimensions of the radio frequency (RF) electrode, and analyzing the direct current (DC) control voltages. As an example of this design procedure, we present a case study with tutorial-like explanations. The proposed design procedure can provide a practical guideline for designing the electrodes of surface ion traps.

Ion traps are a foundational technology in quantum information processing, precision spectroscopy and foundational physics tests. At the heart of their performance is the inhibition of micromotion, an oscillation of ions through imperfect trapping potentials, that restricts the laser cooling efficiency, coherence times, and the accuracy of measurements. The paper provides a systematic computational analysis of four different electrode geometries (Linear Paul, Segmented, Surface and Ring) in 24 different RF / DC configurations (C01-C24) and 13 performance parameters that comprise trap depth (0.62 1.48 eV), radial secular frequency (1,100 1 Multi-objective optimization with weighted scoring of these metrics indicates that Ring trap geometry scores the highest total (80.2/100), followed by Linear Paul (72.0), Segmented (67.0) and Surface (55.1) configurations. ANOVA (one-way) statistically verified the presence of statistically significant inter-geometry differences in micro-motions amplitude (F = 18.43, p < .001) and cooling efficiency (F = 22.17, p < .001), with Tukey HSD post-hoc revealed that the most significant difference was between the Ring and the Surface. The Pearson correlation analysis shows that RF drive voltage and micromotion amplitude (r = -0.94 to -0.99) and cooling efficiency and micromotion (r = -1.00) have near-perfect inverse correlations, which prove that the quality of confinement is regulated by electrode geometry, RF amplitude, and spacing. These results give quantitative design principles of next-generation ion traps in quantum computing and atomic clock. Keywords: ion trap, micromotion minimization, RF/DC electrode optimization, laser cooling, Mathieu stability, secular frequency, quantum computing

The integration of photonic components into surface ion traps provides a scalable approach for trapped-ion quantum computing, sensing, and metrology, enabling compact systems with enhanced stability and precision. However, the introduction of optical apertures in the trap electrodes can distort the trapping electric field. This can lead to excess micromotion and ion displacement, which degrade the performance of quantum logic operations and optical clocks. In this work, we systematically investigate the electric field distortion in a surface ion trap with integrated waveguides and grating couplers that require apertures in the surface electrode using finite element method simulations. We analyze methods to reduce these distortions by exploiting symmetries and transparent conductive oxide materials.