Chaotic and regular behavior of a trapped ion interacting with a laser field

We study analytically and numerically the motion of a trapped two-level ion in the presence of a resonant laser field. Using a semiclassical description, we find that for sufficiently strong laser fields atomic motion becomes chaotic for a wide range of parameters and initial conditions. The traces of chaotic motion are reflected in the population inversion of the trapped ion, and thus could be observed by using the quantum jump technique.