Collapse and revival of entanglement of two interacting qubits

Coherent control of quantum dynamics by phase-manipulation of the driving fields, has long been established as an essential tool for state-selective preparation of systems. On the other hand, the basic manipulations of qubits in most physical realizations of quantum-computation devices use Rabi pulses that operate on the Bloch sphere, particularly for weakly-coupled, slow-decoherent systems. In this work we analyze the role of phase-control and phase-dependence of Rabi pulses that prepare Bell states in a system of distinguishable qubits interacting in a harmonic trap. We show that the population dynamics and the properties of the entanglement exhibit a strong dependence to the relative phase. For coherent phonon distributions, collapse and full revival of entanglement occur, while for thermal distributions, except for a few "protected" phases, decoherence with partial revivals are observed.