Dynamics of a trapped ion driven by stochastic optical processes

The probability distributions for the ground and excited states of a two- level ion in a harmonic trap are studied. The incoming photons excite the ion which relaxes back to its ground state by either spontaneous or stimulated emission. The authors assume the arrival times of the photons is described by a Poisson process. Solutions of the model are obtained by numerical and analytical methods. The results obtained are similar to those of quantum mechanical computations for atoms in radiation fields, in the limit of heavy particles. The confinement of small clusters of ions in potential wells, or traps, has been the subject of intense study in recent years, especially since the demonstration by Neuhauser et al. of optical detection of individual ions. The possibility of studying the behavior of small numbers of ions may help the understanding of the mechanisms involved in the phase transition between ordered, crystal-like states and chaotic, disorganized motion