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arXiv:1906.06489 · Physical Review A

Distance scaling and polarization of electric-field noise in a surface ion trap

Da An, Clemens Matthiesen, Erik Urban, Hartmut Häffner

Published Dec 3, 2019• 17 citations
arXivHTMLPDF

Abstract

We probe electric-field noise in a surface ion trap for ion-surface distances $d$ between 50 and 300 \textmu{}m in the normal and planar directions. We find the noise distance dependence to scale as ${d}^{\ensuremath{-}2.6}$ in our trap and a frequency dependence which is consistent with $1/f$ noise. Simulations of the electric-field noise specific to our trap geometry provide evidence that we are not limited by technical noise sources. Our distance scaling data is consistent with a noise correlation length of about 100 \textmu{}m at the trap surface, and we discuss how patch potentials of this size would be modified by the electrode geometry.

DOI
10.1103/physreva.100.063405

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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 ddd 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.
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, ddd, 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−4d^{-4}d−4 dependence currently found by most experiments and models, but also predicts geometry-driven deviations from this trend.
In this work we present a model where we take explicitly into account the spatial dependence of the electric field noise density above a surface, introducing a characteristic length not yet considered in previous models: the correlation length, zeta of the noisy potential on the surface. In that picture, the noise arise from finite size sources distributed randomly on the surface. We show that this simple model accounts for the behavior of electric field noise scaling on the whole range covered by both ion heating measurements and cantilever-based measurements. We propose that this correlation length could be related to the characteristic size of the patches, opening a way to the control of noise intensity by engineering the material properties.
The electric-field noise affecting quantum logic gates in surface-electrode ion traps is studied as a function of trapping frequency, electrode temperature, and distance ddd between ion and surface. The finding that the noise scales as 1/d41/{d}^{4}1/d4 eliminates various surface-noise models that have been proposed to explain the anomalous ion heating observed in this type of trap.
Electric-field noise from ion-trap electrode surfaces can limit the fidelity of multiqubit entangling operations in trapped-ion quantum information processors and can give rise to systematic errors in trapped-ion optical clocks. The underlying mechanism for this noise is unknown, but it has been shown that the noise amplitude can be reduced by energetic ion bombardment, or ``ion milling,'' of the trap electrode surfaces. Using a single trapped 88Sr+^{88}\mathrm{Sr}^{+}88Sr+ ion as a sensor, we investigate the temperature dependence of this noise both before and after ex situ ion milling of the trap electrodes. Making measurements over a trap electrode temperature range of 4 K to 295 K in both sputtered niobium and electroplated gold traps, we see a marked change in the temperature scaling of the electric-field noise after ion milling: power-law behavior in untreated surfaces is transformed to Arrhenius behavior after treatment. The temperature scaling becomes material-dependent after treatment as well, strongly suggesting that different noise mechanisms are at work before and after ion milling. To constrain potential noise mechanisms, we measure the frequency dependence of the electric-field noise, as well as its dependence on ion-electrode distance, for niobium traps at room temperature both before and after ion milling. These scalings are unchanged by ion milling.
Electric-field noise from ion-trap electrode surfaces can limit the fidelity of multiqubit entangling operations in trapped-ion quantum information processors and can give rise to systematic errors in trapped-ion optical clocks. The underlying mechanism for this noise is unknown, but it has been shown that the noise amplitude can be reduced by energetic ion bombardment, or “ion milling,” of the trap electrode surfaces. Using a single trapped ⁸⁸Sr⁺ ion as a sensor, we investigate the temperature dependence of this noise both before and after ex situ ion milling of the trap electrodes. Making measurements over a trap electrode temperature range of 4 K to 295 K in both sputtered niobium and electroplated gold traps, we see a marked change in the temperature scaling of the electric-field noise after ion milling: power-law behavior in untreated surfaces is transformed to Arrhenius behavior after treatment. The temperature scaling becomes material-dependent after treatment as well, strongly suggesting that different noise mechanisms are at work before and after ion milling. To constrain potential noise mechanisms, we measure the frequency dependence of the electric-field noise, as well as its dependence on ion-electrode distance, for niobium traps at room temperature both before and after ion milling. These scalings are unchanged by ion milling.