Protecting Entanglement via the Quantum Zeno Effect

We study the exact entanglement dynamics of two atoms in a lossy resonator. Besides discussing the steady-state entanglement, we show that in the strong coupling regime the system-reservoir correlations induce entanglement revivals and oscillations and propose a strategy to fight against the deterioration of the entanglement using the quantum Zeno effect.

Figure 1

Stationary concurrence as a function of the relative coupling constant $r_1$ and of the initial separability $s$ of the state, for (a) $\varphi =0$, and (b) $\varphi =\pi$. In the first case, the maximum of $C_s$ is achieved for asymmetrical couplings: at $r_1\simeq 0.87$ for $s=1$, and at $r_1\simeq 0.5$ for $s=-1$. In the second case the maximum is achieved for $|\psi (0)⟩=|{\psi }_{-}⟩$. We point out that these plots are independent of $\lambda$.

Figure 2

Time evolution of the concurrence in the bad cavity limit ($R=0.1$, top plots) and good cavity limit ($R=10$, bottom plots), with (a) $s=1$, and (b) $s=0$, both with $\varphi =0$, for the cases of (i) maximal stationary value, $r_1=0.87$ (solid line), (ii) symmetrical coupling $r_1=1/\sqrt{2}$ (dot-dashed line), and iii) only one coupled atom $r_1=0$, 1 (dotted line). The insets show the initial quadratic behavior of the concurrence for $R=0.1$.

Figure 3

Time evolution of the concurrence, for $s=0$ and $r=1/\sqrt{2}$, in the absence of measurements (solid line) and in the presence of measurements performed at intervals (a) $\lambda T=5$, 1, 0.1 (dashed, dotted, and dot-dashed lines, respectively) with $R=0.1$ (weak coupling) and (b) $\lambda T=0.01$, 0.005, 0.001 (dashed, dotted, and dot-dashed lines, respectively) with $R=10$ (strong coupling).