We study the dynamical behaviour of the ionic inversion in a trapped ion system in running-wave lasers, and wediscuss the properties of entanglement between the ion and phonons and the statistics of the vibrational phonon field.It is shown that the appearance of the super-revivals of the ion inversion is dependent on the initial parameters of thevibrational phonon field. The Schrolinger cat and sub-Poissonian statistics of the phonon field can be also exhibited inthis system for suitable initial values.