arXiv 0711.09422007-11-06quant-ph

玻色-爱因斯坦凝聚体相变中的纠缠

Entanglement in the Bose-Einstein condensate phase transition

Libby Heaney

备注：: 9 pages, 5 figures

摘要：

我们确定了在临界温度凝聚附近的固定粒子数的玻色气体中空间区域之间的纠缠行为。在玻色-爱因斯坦凝聚体（BEC）的相变中发展了长程关联，本文的目的是找出空间相干是否意味着纠缠。我们使用纠缠的纯度度量来导出一个纠缠见证，它可以检测BEC中两个空间区域之间的纠缠。结果表明，两个区域之间的空间相干性是必要的纠缠与相干性和纠缠变得等同，只有当区域占据整个封闭体积的气体。玻色子占据区域的概率是影响纠缠量的唯一其他参数。我们计算了雪茄形谐振势中两个区域间的纠缠量，发现纠缠量随温度的降低而增加。第二个纠缠见证来自三个区域之间的空间纠缠，每对区域之间的空间相干性是纠缠的前兆。结果表明，当玻色子占据三个区域的概率相等时，纠缠量最大的态出现。

英文摘要：

We determine the behaviour of entanglement between regions of space in a Bose gas of fixed particle number around the critical temperature condensation. Long-range correlations develop in the Bose-Einstein condensate (BEC) phase transition and the aim here is to find out whether spatial coherence alone implies entanglement. We use a purity measure of entanglement to derive an entanglement witness that detects entanglement between two regions of space in the BEC. It is shown that spatial coherence between the two regions is necessary for entanglement with coherence and entanglement becoming equivalent only when the regions occupy the entire confining volume of the gas. The probabilities for Bosons to occupy the regions is the only other parameter that influences the amount of entanglement. We calculate explicitly the amount of entanglement between two regions for a cigar-shaped harmonic potential and find that it increases with decreasing temperature. A second entanglement witness is derived for entanglement between three regions of space, where again spatial coherence between each pair of regions is precursor to entanglement. It is shown that the state with the maximum amount of entanglement occurs when the probabilities for the Bosons to occupy the three regions are equal.

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