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Title: Incoherent time evolution on a grid of Landau-Zener anticrossings

Abstract

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.

Authors:
;  [1]
  1. Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506-0055 (United States)
Publication Date:
OSTI Identifier:
142642
DOE Contract Number:  
FG05-92ER14267
Resource Type:
Journal Article
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 49; Journal Issue: 3; Other Information: PBD: Mar 1994
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; ATOMS; LANDAU-ZENER FORMULA; STARK EFFECT; RYDBERG STATES; ELECTRIC FIELDS; CONFIGURATION MIXING; SENSITIVITY ANALYSIS

Citation Formats

Harmin, D A, and Price, P N. Incoherent time evolution on a grid of Landau-Zener anticrossings. United States: N. p., 1994. Web. doi:10.1103/PhysRevA.49.1933.
Harmin, D A, & Price, P N. Incoherent time evolution on a grid of Landau-Zener anticrossings. United States. https://doi.org/10.1103/PhysRevA.49.1933
Harmin, D A, and Price, P N. Tue . "Incoherent time evolution on a grid of Landau-Zener anticrossings". United States. https://doi.org/10.1103/PhysRevA.49.1933.
@article{osti_142642,
title = {Incoherent time evolution on a grid of Landau-Zener anticrossings},
author = {Harmin, D A and Price, P N},
abstractNote = {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.},
doi = {10.1103/PhysRevA.49.1933},
url = {https://www.osti.gov/biblio/142642}, journal = {Physical Review A},
number = 3,
volume = 49,
place = {United States},
year = {1994},
month = {3}
}