  he dynamical properties of quantum entanglement in a time-dependent
three-level-trapped ion interacting with a laser field are studied in terms of
the reduced-density linear entropy considering two specific initial states of
the field. Allowing the instantaneous position of the center-of-mass motion of
the ion to be explicitly time-dependent, it is shown that either sudden death
of entanglement or survivability of quantum entanglement can be obtained with a
specific choice of the initial state parameters. The difference in evolution
picture corresponding to the multi-quanta processes is discussed.
