Abstract
The effect of random fields on the internal dynamics of trapped ions is studied analytically. General characteristics of the dependence of the dephasing on the noise statistics are identified: the form of the initial decay of the coherences is determined by the probability distribution; effects of noise color, in particular, collapses and revivals rooted in spectral concentration of the fluctuations, are apparent in a transient regime; at large times, exponential decay sets in for widely different noise properties. The study is particularized to magnetic-field fluctuations: features distinctive of the linear and quadratic Zeeman shifts are traced. The scaling of the dephasing with the number of ions is analyzed; the implications for the realization of decoherence-free states are discussed.
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