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
± 0.5
%, and the positional error of ions was limited to less than 1.2
μm, all surpassing those achieved by existing methodologies.
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.