Dynamical complexity of driven two-level systems. I. External driving by a given laser field

We treat the general dynamic behavior of an externally driven two-level atom with underlyingSU(2) symmetry in the context of dynamical-systems theory. The temporal evolution of an atom driven by a circularly polarized bichromatic laser field is shown to be regular by calculating the power spectra and the stroboscopic phase portraits in terms of theSU(2) group parameters. In contrast to that, the atomic dynamics is shown to be irregular (ergodic) in the case of a linearly polarized bichromatic laser field. Exhibiting a rich variety of regular and irregular motion, an externally drivenSU(2) dynamical system cannot be truly chaotic in the sense of sensitivity to the initial conditions.