宏观系统量子纠缠存在么？

　　薛定谔猫这个理想实验应该是广为人知了。以前人们只是认为这是个理想的东西，是哲学意义上的探讨。可是现在物理学家们已经开始对这个问题进行了深入的研究，它已经是一个很值得探讨的物理问题了。
我了解到，为了解释为什么宏观物体无法出现薛定谔猫态(也就是纠缠态)，物理学家专门计算了宏观系统的退相干时间，发现它非常的小，几乎是一瞬间就消去了相干的特性。这样我们就无法在宏观系统中观察到薛定谔猫态了。所谓退相干，就是说在环境等外部因素的影响下，相互纠缠的量子系统演变到不纠缠这么一个过程。大家普遍认为这个退相干的过程就是宏观物体观察不到薛定谔猫态的原因。其实，还有许多其它的理论也用来解释量子到经典的转变。比如，自发波函数塌缩模型¹，引力导致的退相干²，等等。如果我们能够想办法减缓退相干，是否意味着有可能观察到宏观量子纠缠呢？
前天arXiv上又贴出了一篇论文讨论一个宏观量子纠缠的问题。这篇论文讨论的是一个腔中的电磁场与其中可以运动的镜子之间的纠缠。具体的细节这里不深究，但是其中的结论很有意思。最重要的结论就是，温度不为零时，纠缠不一定就会很快的消失。如果场对镜子的压力很大的话，那么除了温度趋于无穷大的情况以外，在其它温度下，仍还会有纠缠。这与以前人们认为的高温会破坏纠缠的想法是矛盾的。而且这里的纠缠随着时间的是在做周期震荡的。如果腔的品质因数Q很高的话，可以认为这个纠缠不会明显的随时间衰退。
宏观的纠缠到底是什么样的，到底存在与否，有什么性质？这些其实人们都不太清楚。上面的这篇论文在这里做了一个很有意思的探讨，厘清了一些模糊的观念。而光与镜子的相互作用，与原子，原子团的相互作用，以及引起的纠缠，对探讨宏观体系的量子纠缠是一条很好的途径。

最后我附上几个介绍纠缠，退相干的网址：

孙昌璞之科普园地

QUbit上对Quantum Entanglement的介绍

S. Ghosh et al., Nature 425 48 (2003).
R. Penrose, in A. Fokas et al. (Eds.), Mathematical Physics 2000 (Imperial College, London, 2000).

Some questions

My boss Prof. Li gave me some questions recently. One of them is whether there is entanglement among the macro-systems. We definitely know that there would be entanglement between the quantum systems, which are micro-scaled. When the system we discussed is too large to be viewed as micro-system, is there entanglement in this system? My boss enlightened me that firstly we should discuss the quantum system, for example, two spins being entangled by a electromagnative wave. We calculate the entanglement between them. Then we add the spin to the system, and calculate the entanglement again. Finally we get the relationship between the entanglement and the number of spins. When the number of spins apoaches to infinity, the micro-system becomes the macro-systems. So we solve the question at the beginning of this entry.

Entanglement witness

Recently I read a article quant-ph/0503037 written by Marcin Wiesniak, Vlato Vedral and Caslav Brukner. Here is the abstract:

We show that, when measured along orthogonal spatial directions, magnetic susceptibility can reveal entanglement between individual constituents of a solid, while magnetisation describes their local properties. We then show that these two thermodynamical quantities satisfy complementary relation in the quantum-mechanical sense. It describes sharing of (quantum) information in the solid between entanglement and local properties of its individual constituents. Magnetic susceptibility is shown to be universal macroscopic entanglement witness that can be applied independently of the model of the solid (without the knowledge of its Hamiltonian).

The most important result of this article, in my opinion, is the quantum complementary relation. That is the sum of the entanglement and the local properties S=frac{langle rightarrow{M}rangle^2}{N^2}. This article also given a criterion to estimate the solid state system contains entanglement or not. If the magnetic susceptibility bigger than a critical value, there must be entanglement in the system. As we know, susceptibility has been experimental routime for long time. So using the result of the article, we can detect the entanglement in the solid system. I think this is an important result. In fact, this article told us that magntetization only described the local feather of a solid, but susceptibility related with the global entanglement of the solid system.

I guess that the localizalbe entanglment(LE) defined in the recent article PRA 71, 042306 (2005) may have some relation with the result of the article above. The lower bound of LE connects with a correlation function. As we kown, susceptibility is some kind of correlation in the solid system. If I dig deeply in this, I think I can reveal this relation.