Incoherent time evolution on a grid of Landau-Zener anticrossings
- Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506-0055 (United States)
The mixing of Rydberg manifolds, induced by a ramped electric field {ital F}({ital t})={ital {dot F}t}, 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 {ital D}=exp({minus}2{pi}{gamma}) and {ital A}=1{minus}{ital D} for diabatic and adiabatic transitions, respectively. The model assumes a core with one nonvanishing quantum defect {mu}{sub 0} and with extremal Stark-level slopes, so that {gamma}={vert_bar}{mu}{sub 0}{vert_bar}{sup 2}/3{ital {dot F}n}{sup 10} for all anticrossings, where the manifolds have principal quantum numbers {ital n} and {ital 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 ({ital D}{r_arrow}1) and adiabatic ({ital D}{r_arrow}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.
- DOE Contract Number:
- FG05-92ER14267
- OSTI ID:
- 142642
- Journal Information:
- Physical Review A, Vol. 49, Issue 3; Other Information: PBD: Mar 1994
- Country of Publication:
- United States
- Language:
- English
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