Coherent time evolution on a grid of LandauZener 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 LandauZener (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 twodimensional grid of isolated anticrossings. The time development of an initially populated state is then governed by twolevel 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 selectivefield ionization.more »
 Authors:

 MaxPlanckInstitut fuer Quantenoptik, HansKopfermannStrasse 1, D85748 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; LANDAUZENER FORMULA; ENERGY LEVELS; TIME DEPENDENCE; SENSITIVITY; ELECTRIC FIELDS
Citation Formats
Harmin, D A, and Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 405060055. Coherent time evolution on a grid of LandauZener 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 405060055. Coherent time evolution on a grid of LandauZener 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 405060055. Tue .
"Coherent time evolution on a grid of LandauZener anticrossings". United States. https://doi.org/10.1103/PhysRevA.56.232.
@article{osti_531766,
title = {Coherent time evolution on a grid of LandauZener anticrossings},
author = {Harmin, D A and Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 405060055},
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 LandauZener (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 twodimensional grid of isolated anticrossings. The time development of an initially populated state is then governed by twolevel 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 selectivefield 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}
}