Atomic motion and dipole-dipole effects on the stability of atom-atom entanglement in Markovian/non-Markovian reservoir

In this paper, we consider the entanglement dynamics of two identical qubits (two-level atoms) accompanied by dipole-dipole interaction within a common reservoir in the strong and weak coupling regimes. We suppose that the qubits move in the reservoir which is at zero temperature. Using the time-dependent Schrodinger equation, the state vector of the qubits-reservoir system is obtained by which we can evaluate the concurrence as a suitable measure of entanglement between the two qubits. The results show that by choosing special initial conditions for the qubits, a different dynamical behavior of entanglement is visible in such a way that entanglement protection occurs. Also, we find that the qubit motion in the absence of dipole-dipole interaction leads to preservation or at least more slowly decay of entanglement. However, in the presence of dipole-dipole interaction with the movement of qubits, different results can be observed which depend on the initial states of the qubits, i.e. entanglement may or may not be protected.