We report a precise search fur correlation effects in linear chains of 2 an
d 3 trapped Ca+ ions. Unexplained correlations in photon emission times wit
hin a linear chain of trapped ions have been reported, which, if genuine, c
ast doubt on the potential of an ion trap to realize quantum information pr
ocessing. We observe quantum jumps from the metastable 3d(2)D(5/2) level fo
r 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 in 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 a
t the level of the experimental errors (1%); and no rank correlations betwe
en the decay times were found with sensitivity to rank correlation coeffici
ents at the level of IRI = 0.024.