Death of entanglement between light and the vibrational motion of a single trapped ion in the
dispersive regime with a reservoir is investigated. It is found that with phase-damped cavity, the
purity of the light-motional states is lost forever, unlike the purity of the ion's internal states
which have regular patterns and they do not decay. The asymptotic behavior of the states of the
light, the ion-motional and the total system fall into a mixed state. The entanglement and purity
have strong sensitivity to the phase damping and the ionic distribution angle. The entanglement
sudden death has been treated as it arises from the e®ect of phase damping on mixed as well as
pure states.