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Physical Review A

Theoretical investigation of electric-field noise emanating from vibrational adatoms

Jiarui Zeng, Xiao-Tong Yan, Yao Yao, Yu‐Jun Zhao, Liang Chen, Mang Feng

Published Aug 23, 2023• 4 citations
Publisher

Abstract

Electric-field noise stemming from surface adsorption of atoms serves as the main factor of anomalous motional heating and decoherence for trapped ions confined in harmonic potentials of surface-electrode traps. However, this also provides a possible way for ions playing as nanosensors to detect surface defects and explore the mechanism of noise. Taking monatomic vibrations on the surface into account, here we calculate the electric-field noise and discuss its spectral properties by utilizing density-functional theory and the incoherent master equation with fitting parameters. We find that most adatoms lead to universal spectral intensity and frequency scaling. Particularly, we discover a colored feature for the weak-binding Ar adatom with the increase of the temperature, which can be attributed to the anharmonic potential and high-lying vibrational states. Our results could be helpful for understanding the mechanism of the surface noise and developing efficient noise-detection methods.

DOI
10.1103/physreva.108.023121

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Electric-field noise stemming from surface adsorption of atoms serves as the main factor of anomalous motional heating and decoherence for trapped ions confined in harmonic potentials of surface-electrode traps. However, this also provides a possible way for ions playing as nanosensors to detect surface defects and explore the mechanism of noise. Taking monatomic vibrations on the surface into account, here we calculate the electric-field noise and discuss its spectral properties by utilizing density-functional theory and the incoherent master equation with fitting parameters. We find that most adatoms lead to universal spectral intensity and frequency scaling. Particularly, we discover a colored feature for the weak-binding Ar adatom with the increase of the temperature, which can be attributed to the anharmonic potential and high-lying vibrational states. Our results could be helpful for understanding the mechanism of the surface noise and developing efficient noise-detection methods.
The decoherence of trapped-ion quantum gates due to heating of their motional modes is a fundamental science and engineering problem. This heating is attributed to electric-field noise arising from the trap-electrode surfaces. In this work, we investigate the source of this noise by focusing on the diffusion of carbon-containing adsorbates on the surface of Au(110). We show by density functional theory, based on detailed scanning probe microscopy, how the carbon adatom diffusion on the gold surface changes the energy landscape and how the adatom dipole moment varies with the diffusive motion. A simple model for the diffusion noise, which varies quadratically with the variation of the dipole moment, predicts a noise spectrum, in accordance with the measured values.
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Abstract In order to realize the full potential of ion trap quantum computers, an improved understanding is required of the motional heating that trapped ions experience. Experimental studies of the temperature-, frequency-, and ion–electrode distance-dependence of the electric field noise responsible for motional heating, as well as the noise before and after ion bombardment cleaning of trap electrodes, suggest that fluctuations of adsorbate dipoles are a likely source of so-called ‘anomalous heating,’ or motional heating of the trapped ions at a rate much higher than the Johnson noise limit. Previous computational studies have investigated how the fluctuation of model adsorbate dipoles affects anomalous heating. However, the way in which specific adsorbates affect the electric field noise has not yet been examined, and an electric dipole model employed in previous studies is only accurate for a small subset of possible adsorbates. Here, we analyze the behavior of both in-plane and out-of-plane vibrational modes of twenty-one adsorbate–electrode combinations within the independent fluctuating dipole model, utilizing accurate first principles computational methods to determine the surface-induced dipole moments. We find the chemical specificity of the adsorbate can change the electric field noise by seven orders of magnitude and specifically that soft in-plane modes of weakly-adsorbed hydrocarbons produce the greatest noise and ion heating. We discuss the dynamics captured by the fluctuating dipole model, namely the adsorbate-dependent turn-on temperature and electric field noise magnitude, and also discuss the model’s failure to reproduce the measured 1/ω noise frequency scaling with a single adsorbate species. We suggest future research directions for improved, quantitatively predictive models based on extensions of the present framework to multiple interacting adsorbates.
The decoherence of trapped-ion quantum gates due to heating of their motional modes is a fundamen-tal science and engineering problem. This heating is attributed to electric-field noise arising from the trap-electrode surfaces. We have investigated the origin of this noise by focusing on the diffusion of carbon-containing adsorbates on the Au(110) surface. We show how the carbon adatom diffusion on the gold surface changes the energy landscape, and how the adatom dipole moment varies with the diffusive motion. A simple model for the diffusion noise, which varies quadratically with the variation of the dipole moment, predicts a noise spectrum, in accord with the measured values.
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 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.