Non-Adiabatic Transitions in a Model Atom Subject to a Linearly Ramped Electric Field

This work concerns transitions between sets of interacting energy levels that model states of a Rydberg atom in a linearly varying electric field. The model Hamiltonian is derived from consideration of the real physical system, and consists of two sets of diabatic states, whose energies are linear in applied field and which interact via constant coupling. The probabilities of transitions between levels are derived and discussed. Analytical transition probabilities are found for some limiting cases, and numerical results are presented and analyzed. Evidence suggests that the probability of a purely diabatic transition is correctly given by the result of a series of isolated Landau-Zener crossings, even when the assumptions that lead to the Landau -Zener formula do not hold. Numerical evidence also suggests a two-manifold generalization of Demkov's "triangle rule": all transitions that are causally forbidden in the case of isolated avoided crossings also have zero probability for the case of overlapping anticrossings.