Manipulating mixed state entanglement between a time-dependent field and a three-level trapped ion

In this paper, we extend earlier investigations (Q.C. Zhou, S.N. Zhu, Opt. Commun. 248 (2005) 437) on the pure state entanglement to the mixed state entanglement. In particular, analysis of the pattern of entanglement arising in the interaction between a three-level trapped ion with a time-dependent frequency interacting with a laser field is presented. By working out an exact analytic solution, we conclusively calculate the mixed state entanglement formula. Numerical calculations under current experimental conditions are carried out. Depending on the initial state of the system and in the presence of a time-dependent interaction, long surviving entanglement between the trapped ion and field can be obtained.