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

Abstract

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 like 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 Ohmic reservoir. We give a stationary analysis of the concurrence and find that the dynamic of non-markovian entanglement concurrence ${\mathcal{C}}_{\rho }(t)$ 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 $k_{B}T=0$, otherwise the concurrence always disappear at finite time when $k_{B}T>0$, which means that 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 ${\mathcal{C}}_{\rho }(t)$ 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.

14 pages, 7 figures

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