相互作用原子链中的量子结构相变
Quantum structural phase transition in chains of interacting atoms
摘要：
一个准一维系统的捕获，排斥相互作用的原子（例如，离子链）表现出从线性链到Z字形结构的结构相变，通过降低横向陷阱电势或增加粒子密度来调节。由于它是一个一维跃迁，它发生在零温度下，因此量子涨落占主导地位。在[Fishman等人，Phys.Rev.B77，064111（2008）]中，示出了通过$ϕ^4$模型来描述接近于线性Z字形不稳定性的系统。我们提出了一个映射的$ϕ^4$场论的著名的伊辛链在一个横向的领域，它表现出一个量子临界点。基于该映射，我们根据系统参数估计了量子临界点。这个估计给出了临界值的横向陷阱频率的量子相变发生，并有一个有限的，可测量的偏离临界点内的经典理论评估。本文提出了一种在足够低的温度T下探测临界陷阱频率的测量方法。我们特别关注被困离子系统，并估计T和粒子间距离的隐含限制。我们的结论是，量子临界行为的实验观察原则上是可行的。
英文摘要：
A quasi one--dimensional system of trapped, repulsively interacting atoms (e.g., an ion chain) exhibits a structural phase transition from a linear chain to a zigzag structure, tuned by reducing the transverse trap potential or increasing the particle density. Since it is a one dimensional transition, it takes place at zero temperature and therefore quantum fluctuations dominate. In [Fishman, et al., Phys. Rev. B 77, 064111 (2008)] it was shown that the system close to the linear-zigzag instability is described by a $ϕ^4$ model. We propose a mapping of the $ϕ^4$ field theory to the well known Ising chain in a transverse field, which exhibits a quantum critical point. Based on this mapping, we estimate the quantum critical point in terms of the system parameters. This estimate gives the critical value of the transverse trap frequency for which the quantum phase transition occurs, and which has a finite, measurable deviation from the critical point evaluated within the classical theory. A measurement is suggested for atomic systems which can probe the critical trap frequency at sufficiently low temperatures T. We focus in particular on a trapped ion system, and estimate the implied limitations on T and on the interparticle distance. We conclude that the experimental observation of the quantum critical behavior is in principle accessible.
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