Properties of entanglement between the two trapped ions

We consider two independent models which consist of an ion interacting with laser field. The influence of the initial degree of entanglement of the two ions on the entanglement of internal states of ions, ion-ion vibration entanglement and ion vibration-ion vibration entanglement is discussed. We examine entanglement via concurrence and negativity, and find that the sum of entanglement between two ions and entanglement between two ion vibration states is conserved. It is shown that entanglement sudden death (ESD) can happen and the less the value of initial degree of entanglement of the two ions is, the longer the ESD time cost. The initial degree of entanglement of the two ions has no influence on the trends of the evolution of entanglement. The less value of the initial degree of entanglement of the two ions is, the smaller the peak value of the entanglement achieved.