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’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 and a dynamical phase unit φ. The resulting probability distributions of levels are given analytically in the form of recursion relations, generating functions, integral representations involving and φ, 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 and a diabatic pattern for in which only certain levels parallel to the initial one are appreciably populated. The sensitivity of the coherent evolution to φ is discussed, along with the relation of this model to others and to selective-field ionization.
- Received 8 August 1996
DOI:https://doi.org/10.1103/PhysRevA.56.232
©1997 American Physical Society