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Chinese Physics Letters

Design Optimization for Anharmonic Linear Surface-Electrode Ion Trap

Wei Liu, Shuming Chen, Ping‐Xing Chen, Wei Wu

Published Nov 1, 2014• 4 citations
Publisher

Abstract

An accurate and rapid method is proposed to optimize anharmonic linear surface-electrode ion trap design. Based on the method, we analyze the impact of the architectural parameters, including the width, number, and applied voltage of prerequisite active electrodes, on the number and spacing of trapped ions. Sets of optimal anharmonic trap design are given. Then the optimal designs are verified by using an ant colony optimization algorithm. The results show that the maximum ion position errors and maximum ion spacing errors are less than 1 μm up to 80. The mean of the maximum errors is nearly linear with respect to the number of trapped ions.

DOI
10.1088/0256-307x/31/11/113701

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An accurate and rapid method is proposed to optimize anharmonic linear surface-electrode ion trap design. Based on the method, we analyze the impact of the architectural parameters, including the width, number, and applied voltage of prerequisite active electrodes, on the number and spacing of trapped ions. Sets of optimal anharmonic trap design are given. Then the optimal designs are verified by using an ant colony optimization algorithm. The results show that the maximum ion position errors and maximum ion spacing errors are less than 1 μm up to 80. The mean of the maximum errors is nearly linear with respect to the number of trapped ions.
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.
The accurate characterization of the spatial electric field generated by electrodes in a surface electrode trap is of paramount importance. In this pursuit, we have identified a simple yet highly precise parametric expression to describe the spatial field of a rectangular-shaped electrode. Leveraging this expression, we introduced an optimization method designed to accurately characterize the axial electric field intensity produced by the powered electrode and the stray field. Distinct from the existing methods, our approach integrates a diverse array of experimental data, including the equilibrium positions of ions in a linear string, the equilibrium positions of single trapped ions, and trap frequencies, to effectively reduce the systematic errors. This approach provides considerable flexibility in voltage settings for data acquisition, making it especially advantageous for surface electrode traps where the trapping height of ion probes may vary with casual voltage settings. In our experimental demonstration, we successfully minimized the discrepancy between observations and model predictions to a remarkable degree. The relative errors of secular frequencies were contained within ±0.5%, and the positional error of ions was constrained to less than 1.2 μm, which surpasses the performance of current methodologies.
The accurate characterization of the spatial potential generated by a planar electrode in a surface-type Paul trap is of great interest. To achieve this, we employ a simple yet highly precise parametric expression to describe the spatial field of a rectangular-shaped electrode. Based on this, an optimization method is introduced to precisely characterize the axial electric field intensity created by the powered electrode and the stray field. In contrast to existing methods, various types of experimental data, such as the equilibrium position of ions in a linear string, equilibrium positions of single trapped ions and trap frequencies, are utilized for potential estimation in order to mitigate systematic errors. This approach offers significant flexibility in voltage settings for data collection, making it particularly well-suited for surface electrode traps where ion probe trapping height may vary with casual voltage settings. In our demonstration, we successfully minimized the discrepancy between experimental observations and model predictions to an impressive extent. The relative errors of secular frequencies were suppressed within ±\pm± 0.5%\%%, and the positional error of ions was limited to less than 1.2 μμμm, all surpassing those achieved by existing methodologies.
The design of surface-electrode ion traps is studied analytically. The classical motion of a single ion in such a trap is described by coupled Mathieu equations. An analytic boundary-value solution for the Laplace equation in three dimensions with a piecewise-constant Dirichlet boundary condition is described. This solution is used to model the electrostatic potential field generated by a series of electrodes lying in a single plane. The model is applied to the problem of designing surface-electrode ion traps, including calculating important trap design parameters such as the center position of the trapped ion, trap depth, and stability parameters. The model is used to determine optimized dimensions for trap electrodes in various cases.
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.
Trapped ions offer long internal state (spin) coherence times and strong interparticle interactions mediated by the Coulomb force. This makes them interesting candidates for quantum simulation of coupled lattices. To this end, it is desirable to be able to trap ions in arbitrary conformations with precisely controlled local potentials. We provide a general method for optimizing periodic planar radio-frequency electrodes for generating ion trapping potentials with specified trap locations and curvatures above the electrode plane. A linear-programming algorithm guarantees globally optimal electrode shapes that require only a single radio-frequency voltage source for operation. The optimization method produces final electrode shapes that are smooth and exhibit low fragmentation. Such characteristics are desirable for practical fabrication of surface-electrode trap lattices.