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New Journal of Physics

Geometry-resolved suppression of patch-potential heating in skeleton-electrode ion traps

Chon-Teng Belmiro Chu, Hao-Chung Chen, Ting Hsu, Hsiang-Yu Lo, M.-S. Chang, Guin-Dar Lin

Published May 15, 2026• 0 citations

Abstract

Abstract We present a quantitative, geometry-resolved framework to evaluate the effects of patch-potential noise in realistic three-dimensional Paul-trap structures. As a concrete application, we analyze a skeleton-electrode architecture and compare its performance against a conventional blade trap under identical ion-to-electrode distances and matched confinement parameters. The skeleton geometry achieves a suppression of motional heating exceeding 50%, with heating rate ratios of Γ skeleton / Γ blade = 0.46 ( 2 ) for the axial mode and 0.47 ( 3 ) for the radial mode. Patch-by-patch heating maps reveal that over 99% of the noise contribution originates from electrode surfaces within 500 μ m of the ion. We identify that axial heating follows a non-monotonic profile, with dominant ‘hotspots’ located at an intermediate distance of approximately 110 μ m. This behavior is driven by the vectorial directionality of the electric-field components, which provide the strongest axial coupling at these intermediate regions. Guided by these maps, we demonstrate a proof-of-principle electrode reconfiguration where segmented gaps are aligned with identified hotspots. This strategy successfully reduces axial heating even when the total electrode surface area increases, confirming that the spatial distribution of noise coupling—rather than total conductor area—is the primary driver of motional heating. These findings establish geometry-guided design as a practical route to suppress heating in trapped-ion platform, and the proposed skeleton architecture is compatible with advanced fabrication techniques, including metal additive manufacturing.

DOI: 10.1088/1367-2630/ae6e99

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Abstract We present a quantitative, geometry-resolved framework to evaluate the effects of patch-potential noise in realistic three-dimensional Paul-trap structures. As a concrete application, we analyze a skeleton-electrode architecture and compare its performance against a conventional blade trap under identical ion-to-electrode distances and matched confinement parameters. The skeleton geometry achieves a suppression of motional heating exceeding 50%, with heating rate ratios of Γ skeleton / Γ blade = 0.46 ( 2 ) for the axial mode and 0.47 ( 3 ) for the radial mode. Patch-by-patch heating maps reveal that over 99% of the noise contribution originates from electrode surfaces within 500 μ m of the ion. We identify that axial heating follows a non-monotonic profile, with dominant ‘hotspots’ located at an intermediate distance of approximately 110 μ m. This behavior is driven by the vectorial directionality of the electric-field components, which provide the strongest axial coupling at these intermediate regions. Guided by these maps, we demonstrate a proof-of-principle electrode reconfiguration where segmented gaps are aligned with identified hotspots. This strategy successfully reduces axial heating even when the total electrode surface area increases, confirming that the spatial distribution of noise coupling—rather than total conductor area—is the primary driver of motional heating. These findings establish geometry-guided design as a practical route to suppress heating in trapped-ion platform, and the proposed skeleton architecture is compatible with advanced fabrication techniques, including metal additive manufacturing.

Electric-field noise is a major source of motional heating in trapped-ion quantum computation. While the influence of trap-electrode geometries on electric-field noise has been studied in patch potential and surface adsorbate models, only smooth surfaces are accounted for by current theory. The effects of roughness, a ubiquitous feature of surface electrodes, are poorly understood. We investigate its impact on electric-field noise by deriving a rough-surface Green's function and evaluating its effects on adsorbate-surface binding energies. At cryogenic temperatures, heating-rate contributions from adsorbates are predicted to exhibit an exponential sensitivity to local surface curvature, leading to either a large net enhancement or suppression over smooth surfaces. For typical experimental parameters, orders-of-magnitude variations in total heating rates can occur depending on the spatial distribution of adsorbates. Through careful engineering of electrode surface profiles, our results suggests that heating rates can be tuned over orders of magnitudes.

We model electric field noise from fluctuating patch potentials on conducting surfaces by taking into account the finite geometry of the ion trap electrodes to gain insight into the origin of anomalous heating in ion traps. The scaling of anomalous heating rates with surface distance

d

is obtained for several generic geometries of relevance to current ion trap designs, ranging from planar to spheroidal electrodes. The influence of patch size is studied both by solving Laplace's equation in terms of the appropriate Green's function as well as through an eigenfunction expansion. Scaling with surface distance is found to be highly dependent on the choice of geometry and the relative scale between the spatial extent of the electrode, the ion-electrode distance, and the patch size. Our model generally supports the ${d}^{\ensuremath{-}4}$ dependence currently found by most experiments and models, but also predicts geometry-driven deviations from this trend.

The development of scalable quantum technologies requires ion-trap architectures that provide strong and stable confinement while minimizing motional heating caused by electric-field noise. Trapped-ion systems offer long coherence times and high-fidelity quantum control; however, anomalous motional heating from electrode surfaces can limit their performance. This study presents a finite-element analysis of a novel inclined ion-trap architecture, focusing on the effects of electrode geometry and blade separation on confinement strength, secular frequencies, motional heating, thermal response, and RF stability. Five trap inclinations were investigated using three-dimensional electrostatic simulations for blade separations of 5 to 35 um. The RF electric-field distribution was used to determine the effective pseudopotential, trap depth, secular frequencies, and normal modes. An empirical electric-field-noise model was then used to estimate the motional heating rate for frequency-noise exponents alpha = 3, 3.5, and 4. The results reveal a trade-off between confinement strength and ion-electrode distance. Blade separations of approximately 25 to 35 um provide a favorable design regime. At 25 um, the predicted heating rate is approximately 127 to 135 quanta per second for alpha = 3, but the RF stability margin is lower (qmax approximately 1.9). At 35 um, the stability is substantially improved (qmax approximately 0.52), while the heating rate increases to approximately 1570 to 1820 quanta per second. These results provide design guidelines for optimizing inclined ion traps for future trapped-ion quantum-information architectures.

We model electric field noise from fluctuating patch potentials on conducting surfaces by taking into account the finite geometry of the ion trap electrodes to gain insight into the origin of anomalous heating in ion traps. The scaling of anomalous heating rates with surface distance,

d

, is obtained for several generic geometries of relevance to current ion trap designs, ranging from planar to spheroidal electrodes. The influence of patch size is studied both by solving Laplace's equation in terms of the appropriate Green's function as well as through an eigenfunction expansion. Scaling with surface distance is found to be highly dependent on the choice of geometry and the relative scale between the spatial extent of the electrode, the ion-electrode distance, and the patch size. Our model generally supports the

d^{-4}

dependence currently found by most experiments and models, but also predicts geometry-driven deviations from this trend.

Microfabricated Paul ion traps show tremendous promise for large-scale quantum information processing. However, motional heating of ions can have a detrimental effect on the fidelity of quantum logic operations in miniaturized, scalable designs. In many experiments, motional heating rates are ascribed solely to anomalous heating, which arises at least in part from electric field noise from the trap surface not attributable to any known mechanisms. Contributions to measured ion heating rates due to technical voltage noise present on the static (DC) and radio frequency (RF) electrodes—i.e., due to voltage sources, amplifiers, and other electrical components—can often be overlooked. We present a reliable method for determining the extent to which motional heating is dominated by technical voltage noise on the DC or RF electrodes. Also, we demonstrate that stray DC electric fields can shift the ion position such that technical noise on the RF electrode can significantly contribute to the motional heating rate. After minimizing the pseudopotential gradient experienced by the ion induced by stray DC electric fields, the motional heating due to RF technical noise can be significantly reduced.

Electric-field noise near ion-trap electrodes limits motional coherence and represents a key obstacle to scaling trapped-ion quantum systems. Here, we investigate how in situ Ar+ sputtering modifies motional heating and dephasing in multi-material surface-electrode traps. Trapped ions serve as local probes of electric-field fluctuations before and after controlled sputtering cycles. The data reveal a non-monotonic dependence of both the dephasing rate and the electric-field noise on the extent of Ar+ sputtering, with coherence initially improving while heating rates increase, followed by a reversal at longer exposures. This behavior highlights the intricate balance between beneficial surface cleaning and detrimental structural modification, driven by changes in surface morphology, redeposition of sputtered material, and diffusion on the surface, underscoring the complex interplay between surface composition and motional stability in multi-material electrode systems. Post-treatment scanning electron microscopy and energy-dispersive X-ray spectroscopy confirm significant modification of the multilayer structure. Technical noise was independently verified to be well below the observed levels. These findings indicate that in situ sputtering modifies surface properties in ways that can either mitigate or enhance electric-field noise, underscoring the need for precise control of material interfaces in next-generation ion-trap architectures.