Influence of statistics on decoherence and quantum Zeno dynamics

We derive a general method to investigate an interacting quantum system whi ch is additionally subjected to jump-like events of negligible duration occ urring at time instants that are distributed according to a given statistic s. Assuming that the latter can be described by a stationary renewal proces s with an arbitrary waiting-time distribution, we consider in particular a Poissonian and a regular statistics as well as a super-Poissonian one. When the statistics of the events is non-Poissonian, the evolution of the syste m turns out to be non-Markovian. To apply our method we study a two-level s ystem being resonantly driven by a classical field and undergoing jump-like phase decoherence (e.g. caused by quantum-nondemolition measurements of th e level population or by phase-destroying collisions). Taking into account the spontaneous decay of the upper level we obtain analytical results for t he steady state which depend on the waiting-time distribution between the d ephasing events. Moreover, for negligible spontaneous decay we investigate the quantum Zeno dynamics induced by the statistically distributed measurin g or dephasing events. We find that a Poissonain distribution of these even ts is still half as effective as a regular one in increasing the lifetime o f the initial state. (C) 2000 Elsevier Science B.V. All rights reserved.