  We report a precise search for correlation effects in linear chains of 2 and
3 trapped Ca+ ions. Unexplained correlations in photon emission times within a
linear chain of trapped ions have been reported, which, if genuine, cast doubt
on the potential of an ion trap to realize quantum information processing. We
observe quantum jumps from the metastable 3d 2D_{5/2} level for several hours,
searching for correlations between the decay times of the different ions. We
find no evidence for correlations: the number of quantum jumps with separations
of less than 10 ms is consistent with statistics to within errors of 0.05%; the
lifetime of the metastable level derived from the data is consistent with that
derived from independent single-ion data at the level of the experimental
errors 1%; and no rank correlations between the decay times were found with
sensitivity to rank correlation coefficients at the level of |R| = 0.024.
