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arXiv 1010.1817quant-ph
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纠缠产生和处理的连续变量方法

Continuous variables approach to entanglement creation and processing

Li-hui Sun, Gao-xiang Li, Zbigniew Ficek

摘要:

我们应用连续变量的方法来研究耦合谐振子与热库相互作用的纠缠动力学,并在位于高Q环形腔中的原子系综中确定性地产生纠缠。在谐振子的情况下,我们表明,一个合适的幺正变换的位置和动量算子将系统转换为一组独立的谐振子,其中只有一个耦合到水库。在密度算子的Wigner表示中,我们发现协方差矩阵具有较小尺寸矩阵的块对角形式。这个简单的属性允许在一定程度上分析地处理这个问题。我们分析了初始纠缠的时间演化,发现由于协方差矩阵元素的运动常数的存在,纠缠可以持续很长时间。在原子系综位于腔内的情况下,注意力集中在创建一个和两个模式的连续变量纠缠态的真空通过施加适当调整的振幅和相位的激光脉冲。脉冲与腔耗散一起准备原子系综的集体模,使其处于所需的纠缠态。

英文摘要:

We apply the continuous variable approach to study entangled dynamics of coupled harmonic oscillators interacting with a thermal reservoir and to a deterministic creation of entanglement in an atomic ensemble located inside a high-Q ring cavity. In the case of harmonic oscillators, we show that a suitable unitary transformation of the position and momentum operators transforms the system to a set of independent harmonic oscillators with only one of them coupled to the reservoir. Working in the Wigner representation of the density operator, we find that the covariance matrix has a block diagonal form of smaller size matrices. This simple property allows to treat the problem to some extend analytically. We analyze the time evolution of an initial entanglement and find that the entanglement can persists for long times due to presence of constants of motion for the covariance matrix elements. In the case of an atomic ensemble located inside the cavity, the attention is focused on creation of one and two-mode continuous variable entangled states from the vacuum by applying laser pulses of a suitably adjusted amplitudes and phases. The pulses together with the cavity dissipation prepare the collective modes of the atomic ensemble in a desired entangled state.

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