标题： 非平衡状态下耦合Tomonaga-Luttinger液体之间的广泛纠缠 显示英文标题

标题： Extensive entanglement between coupled Tomonaga-Luttinger liquids in and out of equilibrium

摘要： 量子纠缠存在于自然界中，但在经典物理中并不存在，因此它从根本上区分了量子理论和经典理论。 虽然对于少体系统可以常规地观察到纠缠，但在量子多体系统中见证纠缠则要困难得多。 在这里，我们理论上研究了沿着纵向轴分割的两个平行且空间分离的汤川-卢廷液体（TLLs）之间的纠缠。 特别是，我们关注一维玻色气体作为TLLs的实现，并研究两种实验相关的场景：有限温度下的隧穿耦合气体以及相干分裂后的气体。 在两种情况下，我们解析计算了对数负性，并确定了一个临界温度，在该温度以下系统是纠缠的。 值得注意的是，这个临界温度在近期的相干分裂实验中是可达到的。 此外，我们通过将对数负性与互信息进行比较，研究了临界温度附近量子关联和经典关联之间的交叉。 我们认为，由相干分裂建立的初始互信息在TLL动力学中被保留，从而防止某些广义吉布斯系综在预热化过程中被达到。 此外，发现对数负性和互信息都随着子系统的长度呈广延性增长。 尽管耦合TLLs之间的基态纠缠已被预测为广延性，但与其它分割方式相比，这种设置在很大程度上被忽视了。 我们的工作将耦合TLLs之间纠缠的研究扩展到了有限温度和非平衡区域，并提供了一种在有限温度下实验检测量子多体系统中广延纠缠的策略。 显示英文摘要

摘要： Quantum entanglement exists in nature but is absent in classical physics, hence it fundamentally distinguishes quantum from classical theories. While entanglement is routinely observed for few-body systems, it is significantly more challenging to witness in quantum many-body systems. Here, we theoretically study entanglement between two parallel and spatially separated Tomonaga-Luttinger liquids (TLLs) partitioned along the longitudinal axis. In particular, we focus on 1D Bose gases as a realization of TLLs and investigate two experimentally relevant situations: tunnel-coupled gases at finite temperatures and after coherent splitting. In both scenarios, we analytically calculate the logarithmic negativity and identify a threshold temperature below which the system is entangled. Notably, this threshold temperature is accessible in near-term coherent splitting experiments. Furthermore, we investigate the crossover between quantum and classical correlations in the vicinity of the threshold temperature by comparing logarithmic negativity with mutual information. We argue that the initial mutual information established by the coherent splitting is conserved in TLL dynamics, thus preventing certain generalized Gibbs ensembles from being reached during prethermalization. Moreover, both logarithmic negativity and mutual information are found to scale extensively with the subsystem's length. Although the ground-state entanglement between coupled TLLs has been predicted to be extensive, this setting is largely overlooked compared to other partitions. Our work extends the study of entanglement between coupled TLLs to finite temperatures and out-of-equilibrium regimes, and provides a strategy towards experimental detection of extensive entanglement in quantum many-body systems at finite temperatures.