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(-2pigamma) and A = 1 - D for diabatic and adiabatic transitions, respectively. The model assumes a core with one nonvanishing quantum defect mu0 and with extremal Stark-level slopes, so that gamma = \mu0\2/3Fn10 for all anticrossings, where the manifolds have principal quantum numbers n and n + 1. Interference effects are ignored, which allows analytical treatment of the system's 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 (D --> 1) and adiabatic (D --> 0) 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.