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Quantum Information and Computation

Modeling ion trap thermal noise decoherence

LeibrandtDavid, YurkeBernard, SlusherRichart

Published Jan 1, 2007• 0 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 tra...
DOI
10.5555/2011706.2011708

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Quantum Information and Computation•Sep 1, 2007•0 citations
The rate at which external random thermal fluctuations drive transitions between, and cause decoherence of, the near ground vibrational (harmonic oscillator) quantum states of trapped cold ions is of crucial importance in relation to quantum computing. Presented here is an estimate of these rates, for a single trapped ion, based on a quantum perturbation approach where an external thermal energy reservoir is electrically coupled to the ion. The results are for a general system, and it is shown that the relevant parameter in the interpretation of experimentally observed heating rates is the correlation time of the fluctuations. The rates due to the fluctuating electric field associated with blackbody radiation are also considered and shown to be negligible.
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.
We present measurements of the motional heating rate of a trapped ion at different trap frequencies and temperatures between $\ensuremath{\sim}0.6$ and 1.5 MHz and $\ensuremath{\sim}4$ and 295 K. Additionally, we examine the possible effect of adsorbed surface contaminants with boiling points below $\ensuremath{\sim}105{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$ by measuring the ion heating rate before and after locally baking our ion trap chip under ultrahigh vacuum conditions. We compare the heating rates presented here to those calculated from available electric-field noise models. We can tightly constrain a subset of these models based on their expected frequency and temperature scaling interdependence. Discrepancies between the measured results and predicted values point to the need for refinement of theoretical noise models in order to more fully understand the mechanisms behind motional trapped-ion heating.
We consider two different kinds of fluctuations in an ion trap potential: external fluctuating electrical fields, which cause statistical movement (``wobbling'') of the ion relative to the center of the trap, and fluctuations of the spring constant, which are due to fluctuations of the ac component of the potential applied in the Paul trap for ions. We write down master equations for both cases and, averaging out the noise, obtain expressions for the heating of the ion. We compare our results to previous results for far-off resonance optical traps and heating in ion traps. The effect of fluctuating external electrical fields for a quantum gate operation (controlled-NOT) is determined and the fidelity for that operation derived.
We analyze numerically the heating of trapped ions due to laser intensity and phase fluctuations when implementing Grover's algorithm and the Quantum Fourier Transform. For a simpler analysis we assume that the stochastic processes are white noise processes and average over each noise as in [Phys. Rev. A. \textbf{57}, 3748, (1998)]. We investigate the fidelity and the heating rate for these algorithms using parameters estimated from experiments, and we can see the order of magnitude difference in the heating rate depending on the quantum algorithms.