Attractor geometry of a quasiperiodically perturbed, two-level atom

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Abstract
We consider the behavior of a two-level atom interacting with a quasiperiodic, resonant field from the perspective of dynamical systems theory. In particular, we analyze the geometry of the phase-space attractor for the atomic system and find that there are basically only two types of attractor geometry, even though the atom’s temporal evolution is very complicated. The dynamics giving rise to these two geometries are differentiated by the degree of adiabaticity associated with the field’s variations, and in the regime of adiabatic dynamics, the attractor shows evidence of a noninteger scaling dimension. This result was unexpected, since IlinearR dynamical systems are not known to give rise to strange attractors. We attribute the attractor’s fractal nature to the scaling behavior of Bloch vector trajectories in the rotating reference frame.