Coherent time evolution on a grid of Landau-Zener anticrossings
- Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching (Germany)
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}
- OSTI ID:
- 531766
- Journal Information:
- Physical Review A, Vol. 56, Issue 1; Other Information: PBD: Jul 1997
- Country of Publication:
- United States
- Language:
- English
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