ANISOTROPIC POTENTIALS IN SURFACE ION TRAPS: DEGRADATION OF HARMONICITY, LIMITATION OF MAXIMUM TRAP FREQUENCIES, AND PERFORMANCE IMPROVEMENTS THROUGH MULTI-ZONE ELECTRODE ARCHITECTURES

Abstract

Surface ion traps are prototypical systems to scaleable quantum computing and precision spectroscopy, but anisotropic trapping potentials inherently degrade the harmonicity of potential wells, thus constraining the available secular trap frequencies, and causing motional decoherence. This paper is a quantitative study of anisotropic potential effects in twelve different surface traps (C01-C12) with single zone linear electrodes up to multi-zone segmented arrays with nine zones. Systematic evaluation was done on data that included trap depth (meV), ion height (um), maximum trap frequency (MHz), harmonicity index (percent), motional heating rate (quanta/s), coherence time (ms), electric field noise spectral density (V 2/m 2Hz) and gate fidelity (percent). Pearson correlation analysis showed that there were significantly high correlations between zone count and harmonicity (r =.935), trap depth (r =.963) and maximum trap frequency (r =.975). A linear regression equation showed that the anisotropy ratio η accounts for the variance of harmonicity due to 99.3 (R 2 =.993, p <.001). The ratio of the anisotropy decreased monotonically with the η = 3.41 in single-zone design to η = 1.11 in nine-zone designs, respectively, as the harmonicity was increased by 72.4 to 96.8. Multi-zone architectures provided a 112.4% increase in trap depth, 383.3% increase in maximum trap frequency and 76.2% decrease in the motional heating rate as compared to the single-zone baseline. Analysis of variance (one-way) showed that the difference in harmonicity between the groups of zones was highly significant (F(5, 6) = 812.34, p < .001). These results give good empirical evidence to the use of multi-zone electrode design as the main approach to counteract the effects of anisotropy on the performance of planar surface ion traps.

Keywords : Surface ion traps, anisotropic potentials, trap harmonicity, multi-zone electrodes, trap frequency, motional heating, quantum computing, secular frequency