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Title: Incoherent time evolution of Rydberg level populations in a Landau-Zener grid

Abstract

The time evolution of two intersecting groups of parallel energy levels, E{sub m} ({tau}) = p{tau} - m{epsilon} and E{sub m {prime}({tau}) = p{tau} + m{prime}{epsilon} = 0,1,2,..., p and {epsilon} constants), is considered as a model of state mixing of interacting Rydberg manifolds by a ramped electric field. Each intersection [m,m{prime}] of the triangular grid of level crossings is treated as an isolated 2-level Landau-Zener anticrossing at energy {1/2} (m{prime}-m){epsilon} with probabilities D and A = 1-D for diabatic and adiabatic transitions, respectively (interference effects are ignored here.) Beginning on the upward-going m = 0 level and following successive time steps {tau}{sup N} = {1/2} N{epsilon}/p (N = 0,1,2,...), a path analysis leads to a distribution of probabilities for arriving at an intersection [m,m{prime}] after N = m +m{prime} previous steps via ({sub m}{sup n}) possible paths. The fastest ramp rates (D {r_arrow} 1} evolve purely diabatically, remaining on the m = 0 level with probability D{sup N}; the slowest ramps (A {r_arrow} 1) follow a purely adiabatic path that switches between mid-grid levels m, m{prime} {approx} {1/2}N with probability A{sup N}. For any but the fastest ramps, however, there is a broad single-humped distribution with average energy E{supmore » (N)}= {1/2} {epsilon} {Sigma}{sub k}{sup N}=1 (D-A){sup k}- population is always concentrated near the center of the interaction region. Its spread in energy grows as N{sup 1/2} at large N but is narrower the larger is A.« less

Authors:
;
Publication Date:
OSTI Identifier:
281217
Report Number(s):
CONF-9305421-
Journal ID: BAPSA6; ISSN 0003-0503; TRN: 96:019142
Resource Type:
Journal Article
Journal Name:
Bulletin of the American Physical Society
Additional Journal Information:
Journal Volume: 38; Journal Issue: 3; Conference: 1993 American Physical Society annual meeting on atomic, molecular, and topical physics, Reno, NV (United States), 16-19 May 1993; Other Information: PBD: May 1993
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; RYDBERG STATES; LANDAU-ZENER FORMULA; TIME DEPENDENCE; ELECTRIC FIELDS

Citation Formats

Price, P N, and Harmin, D A. Incoherent time evolution of Rydberg level populations in a Landau-Zener grid. United States: N. p., 1993. Web.
Price, P N, & Harmin, D A. Incoherent time evolution of Rydberg level populations in a Landau-Zener grid. United States.
Price, P N, and Harmin, D A. Sat . "Incoherent time evolution of Rydberg level populations in a Landau-Zener grid". United States.
@article{osti_281217,
title = {Incoherent time evolution of Rydberg level populations in a Landau-Zener grid},
author = {Price, P N and Harmin, D A},
abstractNote = {The time evolution of two intersecting groups of parallel energy levels, E{sub m} ({tau}) = p{tau} - m{epsilon} and E{sub m {prime}({tau}) = p{tau} + m{prime}{epsilon} = 0,1,2,..., p and {epsilon} constants), is considered as a model of state mixing of interacting Rydberg manifolds by a ramped electric field. Each intersection [m,m{prime}] of the triangular grid of level crossings is treated as an isolated 2-level Landau-Zener anticrossing at energy {1/2} (m{prime}-m){epsilon} with probabilities D and A = 1-D for diabatic and adiabatic transitions, respectively (interference effects are ignored here.) Beginning on the upward-going m = 0 level and following successive time steps {tau}{sup N} = {1/2} N{epsilon}/p (N = 0,1,2,...), a path analysis leads to a distribution of probabilities for arriving at an intersection [m,m{prime}] after N = m +m{prime} previous steps via ({sub m}{sup n}) possible paths. The fastest ramp rates (D {r_arrow} 1} evolve purely diabatically, remaining on the m = 0 level with probability D{sup N}; the slowest ramps (A {r_arrow} 1) follow a purely adiabatic path that switches between mid-grid levels m, m{prime} {approx} {1/2}N with probability A{sup N}. For any but the fastest ramps, however, there is a broad single-humped distribution with average energy E{sup (N)}= {1/2} {epsilon} {Sigma}{sub k}{sup N}=1 (D-A){sup k}- population is always concentrated near the center of the interaction region. Its spread in energy grows as N{sup 1/2} at large N but is narrower the larger is A.},
doi = {},
url = {https://www.osti.gov/biblio/281217}, journal = {Bulletin of the American Physical Society},
number = 3,
volume = 38,
place = {United States},
year = {1993},
month = {5}
}