Incoherent time evolution on a grid of Landau-Zener anticrossings

The mixing of Rydberg manifolds, induced by a ramped electric field F(t)=Ft, is modeled by interactions among two intersecting groups of parallel energy levels. The levels form a grid, each node of which is treated as an isolated two-level Landau-Zener anticrossing, characterized by probabilities D=exp(-2) and A=1-D for diabatic and adiabatic transitions, respectively. The model assumes a core with one nonvanishing quantum defect 0 and with extremal Stark-level slopes, so that =02/3Fn10 for all anticrossings, where the manifolds have principal quantum numbers n and n+1. Interference effects are ignored, which allows analytical treatment of the systems evolution using path statistics or recursion relations. An initially populated edge state leads to a single-humped distribution of level populations. Analytical expressions are found for the probability distribution as a function of time, as well as its average and standard deviation. Limiting forms of the distribution at large times and in the diabatic (D1) and adiabatic (D0) limits are also given. These features are contrasted with those of a random walk. The relevance of the model to selective-field ionization is discussed. © 1994 The American Physical Society.