Entanglement sudden birth of two trapped ions interacting with a time-dependent laser field

We describe some new features of quantum entanglement in two three-level trapped ions confined in a one-dimensional harmonic potential, allowing the instantaneous position of the centre-of-mass motion of the ions to be explicitly time dependent. By solving the exact dynamics of the system, we show how survivability of the quantum entanglement is determined by a specific choice of the initial state settings. In particular, we discuss the underlying conditions that may lead to the phenomena of entanglement sudden birth (delayed creation of entanglement) and sudden death (non-smooth finite-time decay).