Incoherent time evolution on a grid of LandauZener 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 twolevel LandauZener 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 Starklevel 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 singlehumped 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 selectivefield ionization is discussed.
 Authors:

 Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 405060055 (United States)
 Publication Date:
 OSTI Identifier:
 142642
 DOE Contract Number:
 FG0592ER14267
 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; LANDAUZENER 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 LandauZener 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 LandauZener 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 LandauZener anticrossings". United States. https://doi.org/10.1103/PhysRevA.49.1933.
@article{osti_142642,
title = {Incoherent time evolution on a grid of LandauZener 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 twolevel LandauZener 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 Starklevel 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 singlehumped 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 selectivefield 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}
}