Single two-level ion in an anharmonic-oscillator trap: Time evolution of the [Formula Presented] function and population inversion

We investigate the time evolution of the population inversion as well as the [Formula Presented] function for center-of-mass motion for a two-level ion, interacting with single-mode laser light field, in an anharmonic-oscillator trap. The anharmonicities of the trap are quantified in terms of the deformation parameter of the [Formula Presented]-analog trap. For [Formula Presented] [Formula Presented] the collapses and revivals of population inversion become well-defined facilitating experimental observation, but for large [Formula Presented] the time dependence of population inversion is completely wiped out. The quasiprobability function shows an atypical behavior with a single peak at [Formula Presented] splitting up into as many as seven fragments (at [Formula Presented]) during collapse and at a later time these segments come together to signal the revival of population inversion. A small degree of anharmonicity is seen to enhance the coherence of the ion-trap system, whereas for large [Formula Presented] ([Formula Presented] in the present context) the coherence is completely lost.