Non-Markovian disentanglement dynamics of a two-qubit system

We investigate the disentanglement dynamics of a two-qubit system in the non-Markovian approach. It is shown that only for weak coupling between the system and environment does an exponential decay of entanglement appear, for certain classes of two-qubit entangled states. When the coupling between qubit and the environment becomes stronger, entanglement sudden death always appears even if the dissipation environment is at zero temperature.

Figure 1

(Color online) The entanglement decay via spontaneous emission of a pair of two-level qubits starting from the initially entangled state $a/3|\downarrow \downarrow ⟩⟨\downarrow \downarrow |+\left(1-a\right)/3|\uparrow \uparrow ⟩⟨\uparrow \uparrow |+1/3\left(|\downarrow \uparrow ⟩+|\uparrow \downarrow ⟩\right)\left(⟨\uparrow \downarrow |+⟨\downarrow \uparrow |\right)$ with $a$ between 0 and 1. the coupling constant of the qubit with the environment ${\alpha }_A={\alpha }_B=0.01$. Here and in the following figures energies ${\Delta }_A$ and ${\Delta }_B$ are expressed in units of ${\omega }_c$, times in units of ${\omega }_c^{-1}$. We assume ${\Delta }_A={\Delta }_B=0.2$.

Figure 2

(Color online) The entanglement decay via spontaneous emission of the qubits with the coupling constants between the qubit and the environment ${\alpha }_A={\alpha }_B=0.05$. The other parameter the same as Fig. 1.

Figure 3

(Color online) The entanglement decay via spontaneous emission of the pair of two-level qubits. The coupling constants of the qubit to the environment ${\alpha }_A={\alpha }_B=0.1$. The other parameter the same as Fig. 1.