Ionization of H Rydberg atoms: Fractals and power-law decay

Concepts from the theory of transient chaos are applied to study the classical ionization process of a one-dimensional model of kicked hydrogen Rydberg atoms. It is proved analytically that for a range of field parameters the associated classical phase space is devoid of regular islands. In this case, the fraction of atoms ${\mathit{P}}_{\mathit{B}}$(t) not ionized after time t decays asymptotically according to ${\mathit{P}}_{\mathit{B}}$(t)∼${\mathit{t}}^{\mathrm{-}\mathrm{\alpha }}$ with α≊1.65. The origin of the algebraic decay can be traced back to the fractal structure of the invariant set of never-ionizing phase-space points, and is explained by the symbolic dynamics of this system, which consists of a countably infinite number of symbols. The algebraic decay is reproduced by an analytically solvable diffusion model that predicts α=3/2. Replacing zero-width δ kicks with smooth finite-width pulses, a subset of phase space is regular. For this case we observe that ${\mathit{P}}_{\mathit{B}}$(t) shows a transition between two power-law regimes with α≊1.65 for short times and α≊2.1 for long times, where the effect of Cantori and regular islands is felt.