Stochastic simulations of the quantum Zeno effect

We perform stochastic simulations of the quantum Zeno effect experiment of the type realized with trapped cooled ions. The results are carefully examined for the case where the experiment is performed on a single atomic particle. The results of the simulations for a single ion exhibit the probabilistic behavior that is required to satisfy the collapse of the wave-packet hypothesis. When a large ensemble of ions is described by the simulations, the results are the same as those produced using the density-matrix method. In this way the stochastic simulation methods provide a link between these two approaches, as they are compatible with each in the appropriate regime. The results are also discussed in terms of what may be observed experimentally given the practical limitations of performing experiments with individual ions.