Non-Markovian entanglement dynamics between two coupled qubits in the same environment

We analyze the dynamics of the entanglement in two independent non-Markovian channels. In particular, we focus on the entanglement dynamics as a function of the initial states and the channel parameters, such as the temperature and the ratio r between omega(0), the characteristic frequency of the quantum system of interest, and omega(c), the cut-off frequency of the Ohmic reservoir. We give a stationary analysis of the concurrence and find that the dynamic of non-Markovian entanglement concurrence C-rho(t) at temperature k(B)T = 0 is different from the k(B)T > 0 case. We find that 'entanglement sudden death' (ESD) depends on the initial state when kBT = 0, otherwise the concurrence always disappears at a finite time when kBT > 0, which means that the ESD must happen. The main result of this paper is that the non-Markovian entanglement dynamic is fundamentally different from the Markovian one. In the Markovian channel, entanglement decays exponentially and vanishes only asymptotically, but in the non-Markovian channel the concurrence C-rho(t) oscillates, especially in the high temperature case. Then an open-loop controller adjusted by the temperature is proposed to control the entanglement and prolong the ESD time.