Correspondence Principle for Many-Body Scars in Ultracold Rydberg Atoms
Correspondence Principle for Many-Body Scars in Ultracold Rydberg Atoms
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DOI：
10.1103/physrevx.11.021021
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发表时间：
2020-06
期刊：
影响因子：
--
通讯作者：
C. J. Turner;Jean-Yves Desaules;Kieran Bull;Z. Papi'c
中科院分区：
文献类型：
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作者：
C. J. Turner;Jean-Yves Desaules;Kieran Bull;Z. Papi'c
量子疤痕理论——对量子独特遍历性的一种显著违背——基于两个互补的支柱：不稳定经典周期轨道的存在以及所谓的准模，即与系统少数本征态强烈重叠的非遍历态。最近，在里德伯原子链的多体环境中，人们对量子疤痕的兴趣重新燃起。虽然先前的理论工作已经使用含时变分原理（TDVP）确定了此类系统的周期轨道，但周期轨道和准模之间的联系一直缺失。在这里，我们为不可积里德伯原子模型提供了一种概念上简单的准模解析构造，并证明当量子涨落恢复到所有阶时，它们源自先前确定的周期轨道的“再量子化”。我们的结果阐明了TDVP经典系统同时扮演平均场近似和系统经典极限的角色，从而能够在里德伯原子链中的波函数疤痕与单粒子量子系统之间建立严格的联系。
The theory of quantum scarring -- a remarkable violation of quantum unique ergodicity -- rests on two complementary pillars: the existence of unstable classical periodic orbits and the so-called quasimodes, i.e., the non-ergodic states that strongly overlap with a small number of the system's eigenstates. Recently, interest in quantum scars has been revived in a many-body setting of Rydberg atom chains. While previous theoretical works have identified periodic orbits for such systems using time-dependent variational principle (TDVP), the link between periodic orbits and quasimodes has been missing. Here we provide a conceptually simple analytic construction of quasimodes for the non-integrable Rydberg atom model, and prove that they arise from a "requantisation" of previously established periodic orbits when quantum fluctuations are restored to all orders. Our results shed light on the TDVP classical system simultaneously playing the role of both the mean-field approximation and the system's classical limit, thus allowing to establish a rigorous link between the wavefunction scarring in the Rydberg atom chains and the single-particle quantum systems.