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arXiv:0804.2665 · Physical Review Letters

Temperature Dependence of Electric Field Noise above Gold Surfaces

Jaroslaw Labaziewicz, Yufei Ge, David R. Leibrandt, Shannon X. Wang, Ruth Shewmon, Isaac L. Chuang

Published Oct 30, 2008• 132 citations
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Abstract

Electric field noise from fluctuating patch potentials is a significant problem for a broad range of precision experiments, including trapped ion quantum computation and single spin detection. Recent results demonstrated strong suppression of this noise by cryogenic cooling, suggesting an underlying thermal process. We present measurements characterizing the temperature and frequency dependence of the noise from 7 to 100 K, using a single Sr+ ion trapped 75 mum above the surface of a gold plated surface electrode ion trap. The noise amplitude is observed to have an approximate 1/f spectrum around 1 MHz, and grows rapidly with temperature as T;{beta} for beta from 2 to 4. The data are consistent with microfabricated cantilever measurements of noncontact friction but do not extrapolate to the dc measurements with neutral atoms or contact potential probes.

DOI
10.1103/physrevlett.101.180602

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Electric field noise produced by the surface of ion trap electrodes reduces the fidelity of quantum computing operations. Despite decades of investigation its microscopic origins remain unclear.This thesis investigates the origins of surface electric field noise by examining its dependence on trap temperature. A set of Al-Cu surface Paul traps are fabricated together and sent to MIT Lincoln Labs (MITLL) and the University of California, Berkeley (UCB). MITLL measures noise from 7 K to room temperature above a first trap and UCB measures noise from room temperature to 590 K above a second trap. The noise measurements from the two experiments are combined to study the noise dependence over the full temperature range from 7-590 K. This is the largest temperature range ever studied using a single trap design and connects the temperature ranges used in all previous studies.We find qualitatively different behaviors at low and high temperatures: from 7-430 K we find that the noise follows the same power-law scaling reported in previous cryogenic studies. At temperatures from 430-590 K, we find that the noise increases much more rapidly than predicted by the power-law scaling. We note a particularly sharp rise in noise at 560 K, which is similar to the sharp rise in noise reported in a previous high-temperature study of a different Al-Cu trap. To determine which physical processes are associated with the change in noise at elevated trap temperatures, we investigate how the material state of the trap electrodes changes when they are heated. We find that the primary physical process associated with the change in noise at high temperature is thermally-activated atom diffusion within the films.This thesis also investigates if the surface structure of room-temperature Au ion traps affects noise levels. We use a heat treatment to restructure the surface of the traps and measure the resulting change in noise. We find that the heat treatment leads to significant changes to the surface structure but causes only a modest change to noise levels. This indicates that the heat-induced changes to the surface do not strongly affect noise. We also note that the noise magnitude observed above these Au traps is state-of-the-art for room-temperature, untreated surface ion traps. This noise level can be explained by modeling the contamination that exists on the trap surface as a dielectric with a loss tangent of tan θ ≈ 0.01.Finally, this thesis investigates the origin of elevated noise levels in one region of a Au surface ion trap. We find that micron-sized particles are located where noise levels are highest, indicating that these particles are likely responsible for the noise. We can explain the magnitude, frequency, and distance dependence of the noise if we treat the particles as a lossy dielectric with a loss tangent tan θ ≈ 0.3.

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Electric field noise from fluctuating patch potentials is a significant problem for a broad range of precision experiments, including trapped ion quantum computation and single spin detection. Recent results demonstrated strong suppression of this noise by cryogenic cooling, suggesting an underlying thermal process. We present measurements characterizing the temperature and frequency dependence of the noise from 7 to 100 K, using a single Sr+ ion trapped 75 mum above the surface of a gold plated surface electrode ion trap. The noise amplitude is observed to have an approximate 1/f spectrum around 1 MHz, and grows rapidly with temperature as T;{beta} for beta from 2 to 4. The data are consistent with microfabricated cantilever measurements of noncontact friction but do not extrapolate to the dc measurements with neutral atoms or contact potential probes.
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.
Electric-field noise is a major limiting factor in the performance of ion traps and other quantum devices. Despite intensive research over the past decade, the nature and cause of electric field noise near surfaces is not well understood. This dissertation reports the high- temperature dependence of electric-field noise above an Al-Cu surface using a trapped 40Ca+ ion as a probe.We employ a novel setup with a surface ion trap mounted on a heater for studies of the temperature dependence of electric-field noise. To characterize the Al-Cu material, we explore the effects of heat treatment through ex situ annealing followed by inspection in a scanning electron microscope. To calibrate the temperature of the trap, we demonstrate the use of thermal imaging for monitoring the temperature of an ion trap in vacuum.The temperature and frequency dependence of electric-field noise above the surface is measured using the heating rate of a single ion in a surface-electrode Paul trap. We find that the heating rate saturates at temperatures greater than 450 K. We find that the frequency dependence shows a 1/f behavior, and has a lower frequency scaling exponent at high temperatures than at room temperature. We show that these results are a reflection of the surface-related noise by eliminating other possible sources of noise.Building on historical data for resistance fluctuations in thin films, we develop the thermally-activated fluctuator model to describe the results. We find that a broad distribution of fluctuators with energy barriers peaked around 0.5 eV accurately models both the temperature and frequency dependence of the electric-field noise measured. We present the interpretation of this model as a way to infer that the cause of electric-field noise in the trap is likely defect motion in the metal surface, connecting the problems faced in ion trapping to a large body of work in solid state physics.
We probe electric-field noise near the metal surface of an ion-trap chip in the temperature range from 295 to 530 K. We observe a nontrivial temperature dependence with the noise amplitude at 1 MHz frequency saturating around 500 K. Measurements of the noise spectrum reveal a $1/{f}^{\ensuremath{\alpha}\ensuremath{\approx}1}$ dependence and a small decrease in $\ensuremath{\alpha}$ between low and high temperatures. This behavior can be explained by considering noise from a distribution of thermally activated two-level fluctuators with activation energies between 0.35 and 0.65 eV. Processes in this energy range may be relevant to understanding electric-field noise in ion traps; for example, defect motion in the solid state and surface adsorbate binding energies. The study of these processes may aid in identification of the origin of excess electric-field noise in ion traps---a major source of ion motional decoherence limiting the performance of surface traps as quantum devices.
Motional heating of ions in microfabricated traps is one of the open challenges hindering experimental realizations of large-scale quantum processing devices. Recently, a series of measurements of the heating rates in surface-electrode ion traps characterized their frequency, distance, and temperature dependencies, but our understanding of the microscopic origin of this noise remains incomplete. In this work we develop a theoretical model for the electric field noise which is associated with a random distribution of adsorbed atoms on the trap electrode surface. By using first-principles calculations of the fluctuating dipole moments of the adsorbed atoms we evaluate the distance, frequency, and temperature dependence of the resulting electric field fluctuation spectrum. Our theory reproduces correctly the ${d}^{\ensuremath{-}4}$ dependence with distance of the ion from the electrode surface and calculates the noise spectrum beyond the standard scenario of two-level fluctuators by incorporating all the relevant vibrational states. Our model predicts a regime of 1/f1/f1/f noise which commences at roughly the frequency of the fundamental phonon transition rate and a thermally activated noise spectrum which for higher temperatures exhibits a crossover as a function of frequency.
Electric field noise produced by the surface of ion trap electrodes reduces the fidelity of quantum computing operations. Despite decades of investigation its microscopic origins remain unclear.This thesis investigates the origins of surface electric field noise by examining its dependence on trap temperature. A set of Al-Cu surface Paul traps are fabricated together and sent to MIT Lincoln Labs (MITLL) and the University of California, Berkeley (UCB). MITLL measures noise from 7 K to room temperature above a first trap and UCB measures noise from room temperature to 590 K above a second trap. The noise measurements from the two experiments are combined to study the noise dependence over the full temperature range from 7-590 K. This is the largest temperature range ever studied using a single trap design and connects the temperature ranges used in all previous studies.We find qualitatively different behaviors at low and high temperatures: from 7-430 K we find that the noise follows the same power-law scaling reported in previous cryogenic studies. At temperatures from 430-590 K, we find that the noise increases much more rapidly than predicted by the power-law scaling. We note a particularly sharp rise in noise at 560 K, which is similar to the sharp rise in noise reported in a previous high-temperature study of a different Al-Cu trap. To determine which physical processes are associated with the change in noise at elevated trap temperatures, we investigate how the material state of the trap electrodes changes when they are heated. We find that the primary physical process associated with the change in noise at high temperature is thermally-activated atom diffusion within the films.This thesis also investigates if the surface structure of room-temperature Au ion traps affects noise levels. We use a heat treatment to restructure the surface of the traps and measure the resulting change in noise. We find that the heat treatment leads to significant changes to the surface structure but causes only a modest change to noise levels. This indicates that the heat-induced changes to the surface do not strongly affect noise. We also note that the noise magnitude observed above these Au traps is state-of-the-art for room-temperature, untreated surface ion traps. This noise level can be explained by modeling the contamination that exists on the trap surface as a dielectric with a loss tangent of tan θ ≈ 0.01.Finally, this thesis investigates the origin of elevated noise levels in one region of a Au surface ion trap. We find that micron-sized particles are located where noise levels are highest, indicating that these particles are likely responsible for the noise. We can explain the magnitude, frequency, and distance dependence of the noise if we treat the particles as a lossy dielectric with a loss tangent tan θ ≈ 0.3.