Mahmoud Abdel-Aty

We explore and develop the mathematics of the two multi-level ions. In particular, 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 center-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.

The dynamical properties of quantum entanglement in two three-level trapped ions interacting with a laser field are studied in terms of the negative eigenvalues of the partial transposition of the density operator. In contrast to the usual belief that destroying the entanglement can be observed due to the environment, it is found that the Stark shift can also produce sudden death of entanglement and long-lived entanglement between the qubits that are prepared initially in separable states or mixed states.

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.

With the reliance in the processing of quantum information on a cold trapped ion, we analyze the entanglement entropy in the ion-field interaction with pair cat states. We investigate a long-living entanglement allowing the instantaneous position of the center-of-mass motion of the ion to be explicitly time dependent. An analytic solution for the system operators is obtained. We show that different nonclassical effects arise in the dynamics of the population inversion, depending on the initial states of the vibrational motion. We study in detail the entanglement degree and demonstrate how the input pair cat state is required for initiating the long living entanglement. This long living entanglement is damp out with an increase in the number difference $q$. Owing to the properties of entanglement measures, the results are checked using another entanglement measure (high order linear entropy).