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arXiv:quant-ph/0002040 · Physical Review A

Heating of trapped ions from the quantum ground state

Q. A. Turchette, D. Kielpinski, B. E. King, Dietrich G. Leibfried, D. M. Meekhof, Christopher J. Myatt, M. A. Rowe, Charles A. Sackett, C. S. Wood, Wayne M. Itano, Christopher R. Monroe, D. J. Wineland

Published May 17, 2000• 543 citations
arXivHTMLPDF

Abstract

We have investigated motional heating of laser-cooled ${}^{9}{\mathrm{Be}}^{+}$ ions held in radio-frequency (Paul) traps. We have measured heating rates in a variety of traps with different geometries, electrode materials, and characteristic sizes. The results show that heating is due to electric-field noise from the trap electrodes that exerts a stochastic fluctuating force on the ion. The scaling of the heating rate with trap size is much stronger than that expected from a spatially uniform noise source on the electrodes (such as Johnson noise from external circuits), indicating that a microscopic uncorrelated noise source on the electrodes (such as fluctuating patch-potential fields) is a more likely candidate for the source of heating.

DOI
10.1103/physreva.61.063418

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We have investigated motional heating of laser-cooled 9Be+{}^{9}{\mathrm{Be}}^{+}9Be+ ions held in radio-frequency (Paul) traps. We have measured heating rates in a variety of traps with different geometries, electrode materials, and characteristic sizes. The results show that heating is due to electric-field noise from the trap electrodes that exerts a stochastic fluctuating force on the ion. The scaling of the heating rate with trap size is much stronger than that expected from a spatially uniform noise source on the electrodes (such as Johnson noise from external circuits), indicating that a microscopic uncorrelated noise source on the electrodes (such as fluctuating patch-potential fields) is a more likely candidate for the source of heating.
We report on ground-state laser cooling of single 111Cd+^{111}\mathrm{Cd}^{+}111Cd+ ions confined in radio-frequency (Paul) traps. Heating rates of trapped ion motion are measured for two different trapping geometries and electrode materials, where no effort was made to shield the electrodes from the atomic Cd\mathrm{Cd}Cd source. The low measured heating rates suggest that trapped 111Cd+^{111}\mathrm{Cd}^{+}111Cd+ ions may be well suited for experiments involving quantum control of atomic motion, including applications in quantum information science.
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.
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 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.
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.
Ion traps are promising architectures for implementing quantum computers, but they suffer from excessive ``anomalous'' ion motional heating that limit their overall coherence and practicality for scalable quantum computing. The exact microscopic origins of anomalous heating remain an open question, but experiments point to adsorbates on trap electrodes as one likely source. Many different models of anomalous heating have been proposed, but these models have yet to pinpoint the atomistic origin of the experimentally observed $1/\ensuremath{\omega}$ electric-field noise scaling seen in ion traps at frequencies between 0.1--10 MHz. In this work, we show that a model based on previously proposed surface-induced dipole fluctuations on adsorbates, but which also incorporates interparticle interaction dynamics through molecular dynamics simulations of up to multiple monolayers of adsorbates, gives rise to $1/\ensuremath{\omega}$ frequency scaling at the MHz frequencies typically employed in ion traps. These results demonstrate that moderate-to-high densities of adsorbates can give rise to a set of activated motions that produce the $1/\ensuremath{\omega}$ noise observed in ion traps and that collective adsorbate motions produce the observed noise spectra that a noninteracting model does not capture.