Sudden death and long-living of entanglement in an ion-trap laser

The 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.