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arXiv 0809.1676quant-ph
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耦合到同一环境的两个振子纠缠演化的动力学相位

Dynamical phases for the evolution of the entanglement between two oscillators coupled to the same environment

Juan Pablo Paz, Augusto J. Roncaglia

摘要:

我们研究了两个振荡器之间的纠缠动力学,这两个振荡器最初是在一般的双模高斯态中准备的,并在耦合到相同的环境中演化。在之前的论文中,我们证明了在长时间限制下纠缠有三个性质不同的动力学阶段:突然死亡,突然死亡和复活以及非突然死亡[Paz & Roncaglia,Phys. Rev. Lett. 100,220401(2008)]。在这里,我们概括和扩展这些结果沿几个方向:我们分析的命运纠缠的环境与一般的谱密度提供了一个完整的表征相应的相图欧姆和亚欧姆环境(我们还分析了超欧姆的情况下,显示这种环境的预期行为是相当不同的)。我们还通过考虑系统与环境之间相互作用的两种不同模型来概括以前的研究(首先我们分析耦合是通过位置的情况,然后我们研究耦合在位置和动量上对称的情况)。最后,我们分析(数值和解析)的情况下,非共振振荡器。在这种情况下,我们表明,最终的纠缠是独立的初始状态,并可能在非常低的温度下是非零的。我们提供了一个自然的解释,我们的结果在一个简单的量子光学模型。

英文摘要:

We study the dynamics of the entanglement between two oscillators that are initially prepared in a general two-mode Gaussian state and evolve while coupled to the same environment. In a previous paper we showed that there are three qualitatively different dynamical phases for the entanglement in the long time limit: sudden death, sudden death and revival and no-sudden death [Paz & Roncaglia, Phys. Rev. Lett. 100, 220401 (2008)]. Here we generalize and extend those results along several directions: We analyze the fate of entanglement for an environment with a general spectral density providing a complete characterization of the corresponding phase diagrams for ohmic and sub--ohmic environments (we also analyze the super-ohmic case showing that for such environment the expected behavior is rather different). We also generalize previous studies by considering two different models for the interaction between the system and the environment (first we analyze the case when the coupling is through position and then we examine the case where the coupling is symmetric in position and momentum). Finally, we analyze (both numerically and analytically) the case of non-resonant oscillators. In that case we show that the final entanglement is independent of the initial state and may be non-zero at very low temperatures. We provide a natural interpretation of our results in terms of a simple quantum optics model.

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