Abstract: The dynamical properties of the population inversion of a trapped ion in standing wave field are studied. The influences of the nonlinear parametersη and the phase of the standing wave field on the collapses and revivals of the ionic inversion are discussed. The results show that the nonlinear parameter η has a great influence on the ion population inversion, namely, when the parameter η increases, the period of the ion population inversion becomes short and the oscillation frequency becomes larger. it is not obvious for the contour of the collapses and revivals of the ion population inversion when η reaches a critical value. In addition, the phase of the standing wave field also shows a significant influence on the ion population inversion.

Key words: quantum optics, population inversion, quantum theory, nonlinear coherent state