Chaotic Behavior of a One-dimensional Model Atom in an Intense Field
  In this paper we describe the rescattering process in optical field ionization through a one-dimensional model, which improves the well-known quasistatic model by adding the smoothed Coulomb potential in its second step. The above-threshold ionization spectra and high-order harmonic generation are calculated from this model. They are qualitatively in agreement with the quantum results and experiments. In particular, we find that this model is characterized by chaotic scattering. Modern nonlinear theory is used to analyze this dynamical system. It is found that singular self-similar fractal structure exists in the phase-dependence energy spectra, and the unstable manifolds constitute the chaotic scattering pattern. Our results also demonstrate a close connection of irregular trajectories with the energy spectra and high-order harmonic generation. We conclude that the chaotic behavior plays an important role in this one-dimensional model of optical field ionization. 
Jie Liu, Shi-Gang Chen, and Bambi Hu (Centre for Nonlinear Studies,   Hong Kong Baptist University, Hong Kong, China)