Abstract
A Quantum Monte Carlo wave function approach is used to rule out the possibility of cooperative effects in the quantum jump statistics of adjacent three-level ions of the type discussed in a series of experiments and theoretical investigations. By deriving analytical results and examining quantum jumps in various subspaces, we track this outcome to the fact that a fast spontaneous decay inhibits dipole-dipole-induced entanglement between the ions developing on a much slower time scale. This inhibition is demonstrated even for weak pumping of the fast transition. The Quantum Monte Carlo calculation thus sheds new light on the controversy arising from the findings of two recent conflicting experiments by Block et al. (Eur. Phys. J. D, 7 (1999) 461) and Donald et al. (Europhys. Lett., 51 (2000) 388).