skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Abstract

A model of the time evolution of two interacting Rydberg manifolds of energy levels subject to a linearly ramped electric field is solved exactly in the Landau-Zener (LZ) approximation. Each manifold{close_quote}s levels are treated as linear in time, parallel, equally spaced, and infinite in number. Their pairwise interactions produce a regular two-dimensional grid of isolated anticrossings. The time development of an initially populated state is then governed by two-level LZ transitions at avoided crossings and adiabatic evolution between them, parametrized by the LZ transition probability D and a dynamical phase unit {var_phi}. The resulting probability distributions of levels are given analytically in the form of recursion relations, generating functions, integral representations involving D and {var_phi}, and in certain limits by Bessel or Whittaker functions. Level populations are mapped out versus location on the grid for a range of cases. Interference effects lead to two principal types of probability distributions: a braiding adiabatic pattern with revivals for small D and a diabatic pattern for D{r_arrow}1 in which only certain levels parallel to the initial one are appreciably populated. The sensitivity of the coherent evolution to {var_phi} is discussed, along with the relation of this model to others and to selective-field ionization.more » {copyright} {ital 1997} {ital The American Physical Society}« less

Authors:
 [1]
  1. Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching (Germany)
Publication Date:
OSTI Identifier:
531766
Resource Type:
Journal Article
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 56; Journal Issue: 1; Other Information: PBD: Jul 1997
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; RYDBERG STATES; LANDAU-ZENER FORMULA; ENERGY LEVELS; TIME DEPENDENCE; SENSITIVITY; ELECTRIC FIELDS

Citation Formats

Harmin, D A, and Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506-0055. Coherent time evolution on a grid of Landau-Zener anticrossings. United States: N. p., 1997. Web. doi:10.1103/PhysRevA.56.232.
Harmin, D A, & Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506-0055. Coherent time evolution on a grid of Landau-Zener anticrossings. United States. https://doi.org/10.1103/PhysRevA.56.232
Harmin, D A, and Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506-0055. Tue . "Coherent time evolution on a grid of Landau-Zener anticrossings". United States. https://doi.org/10.1103/PhysRevA.56.232.
@article{osti_531766,
title = {Coherent time evolution on a grid of Landau-Zener anticrossings},
author = {Harmin, D A and Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506-0055},
abstractNote = {A model of the time evolution of two interacting Rydberg manifolds of energy levels subject to a linearly ramped electric field is solved exactly in the Landau-Zener (LZ) approximation. Each manifold{close_quote}s levels are treated as linear in time, parallel, equally spaced, and infinite in number. Their pairwise interactions produce a regular two-dimensional grid of isolated anticrossings. The time development of an initially populated state is then governed by two-level LZ transitions at avoided crossings and adiabatic evolution between them, parametrized by the LZ transition probability D and a dynamical phase unit {var_phi}. The resulting probability distributions of levels are given analytically in the form of recursion relations, generating functions, integral representations involving D and {var_phi}, and in certain limits by Bessel or Whittaker functions. Level populations are mapped out versus location on the grid for a range of cases. Interference effects lead to two principal types of probability distributions: a braiding adiabatic pattern with revivals for small D and a diabatic pattern for D{r_arrow}1 in which only certain levels parallel to the initial one are appreciably populated. The sensitivity of the coherent evolution to {var_phi} is discussed, along with the relation of this model to others and to selective-field ionization. {copyright} {ital 1997} {ital The American Physical Society}},
doi = {10.1103/PhysRevA.56.232},
url = {https://www.osti.gov/biblio/531766}, journal = {Physical Review A},
number = 1,
volume = 56,
place = {United States},
year = {1997},
month = {7}
}