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Quantum Information and Computation

Modeling ion trap thermal noise decoherence

David R. Leibrandt, Bernard Yurke, Richard E. Slusher

Published Jan 1, 2007• 16 citations
Publisher

Abstract

We present a detailed analysis of ion heating caused by thermal fluctuation noise in ion traps. The results of the analysis are used to estimate thermal noise ion heating rates for a variety of trap electrode configurations and materials, including recent scalable multiplexed planar ion trap proposals based on silicon VLSI technology. We find that minimizing thermal noise ion heating places severe constraints on the design and materials used for ion traps.

DOI
10.26421/qic7.1-2-2

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We present a detailed analysis of ion heating caused by thermal fluctuation noise in ion traps. The results of the analysis are used to estimate thermal noise ion heating rates for a variety of trap electrode configurations and materials, including recent scalable multiplexed planar ion trap proposals based on silicon VLSI technology. We find that minimizing thermal noise ion heating places severe constraints on the design and materials used for ion traps.
Abstract Ions in surface-electrode ion traps are susceptible to heating due to various noise sources, which can degrade coherence and fidelity. This study investigates the heating mechanisms in surface-electrode ion traps, with a focus on the role of dielectric materials and the effectiveness of shielding techniques. Using the fluctuation-dissipation theorem and finite element simulations, we demonstrate that a metallic shielding layer beneath the dielectric layer can reduce the heating rate by five orders of magnitude. Additionally, indenting the dielectric layer supporting the electrodes further decreases the heating rate by minimizing the exposed area in the ion’s field of view. Experimental results validate these findings, showing a three-order-of-magnitude reduction in heating rates for traps with a shielding layer. Our work provides a comprehensive methodology for assessing and minimizing dielectric heating, offering practical design insights for improving the performance of trapped ion quantum systems.
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.
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.
The electromagnetic manipulation of isolated ions has led to many advances in atomic physics, from laser cooling to precision metrology and quantum control. As technical capability in this area has grown, so has interest in building miniature electromagnetic traps for the development of large-scale quantum information processors. This thesis will primarily focus on using microfabrication techniques to build arrays of miniature ion traps, similar to techniques used in fabricating high component density microprocessors. A specific focus will be on research using a gallium arsenide/aluminum gallium arsenide heterostructure as a trap architecture, as well as the recent testing of different ion traps fabricated at outside foundries. The construction and characterization of a conventional ceramic trap capable of shuttling an ion through a junction will also be detailed, and reveal the need for moving towards lithographically fabricated traps. Combined, these serve as a set of proof-of-principle experiments pointing to methods for designing and building large scale arrays of ion traps capable of constituting a quantum information processor. As traps become smaller, electrical potentials on the electrodes have greater influence on the ion. This not only pertains to intentionally applied voltages, but also to deleterious noise sources, such as thermal Johnson noise and the more significant ``patch potential" noise, which both cause motional heating of the ion. These problematic noise sources dovetail with my thesis research into trap miniaturization since their effects become more pronounced and impossible to ignore for small trap sizes. Therefore characterizing them and investigating ways to suppress them have become an important component of my research. I will describe an experiment using a pair of movable needle electrodes to measure the ion heating rate corresponding to the harmonic frequency of the trap, the ion-electrode distance, and the electrode temperature. This information is used for characterizing the fluctuating potentials and exploring the possibility of suppressing motional heating by cooling the trap electrodes. This source of noise is also observed in other systems, and its characterization could potentially improve other precision experiments, such as those measuring deviations in the gravitational inverse square law with proximate masses.
Electric-field noise in microfabricated surface ion traps contributes to gate errors in trapped-ion quantum computers, but this noise has been challenging to predict. Here, we present a method to predict the electric-field noise arising from fluctuations in the bulk of dielectric and metallic materials. The method is valid for arbitrary trap geometries, and the only relevant material property is energy loss. We apply it to an ion trap with an electrically floating electrode and find the contribution from dielectrics to be dominant. Our model predicts the observed noise for this trap within a factor of four. In addition, we apply our model to typical surface trap designs and analyze how the electrode structures shield the noise.