近日，美国加州大学的Jairo Velasco Jr&Zhehao Ge及其研究团队取得一项新进展。经过不懈努力，他们实现了石墨烯量子点中相对论量子伤痕的直接可视化。相关成果已于2024年11月27日在国际权威学术期刊《自然》上发表。

该研究团队展示了通过使用原位石墨烯量子点（GQD）和波函数映射技术，在扫描隧道显微镜下以纳米空间分辨率和毫电子伏能量分辨率成像狄拉克电子的量子疤痕。具体来说，研究人员发现在他们体育场形状的GQDs中，概率密度以双扭线∞形和条纹状模式的形式增强。

这两个特征都显示出相等的能量间隔递推，与相对论量子伤痕的预测一致。通过结合经典和量子模拟，研究人员证明了观测到的模式对应于他们体育场形状的GQD中存在的两个不稳定的周期轨道，从而证明它们都是量子伤痕。

除了提供量子疤痕的明确视觉证据外，这项研究工作还提供了对相对论混沌量子系统中量子-经典对应关系的见解，并为最近提出的其他疤痕组分（如微扰诱导疤痕、手性疤痕和反疤痕）的实验研究铺平了道路。

据悉，量子疤痕是指沿着不稳定经典周期轨道具有增强概率密度的本征态。这一概念首次提出于40年前，疤痕是一种特殊的本征态，它们反常地违背了其经典对应体为混沌的量子系统中的遍历性。尽管疤痕具有重要意义且研究历史悠久，但在量子系统中直接观测到它们仍然是一个开放领域。

附：英文原文

Title: Direct visualization of relativistic quantum scars in graphene quantum dots

Author: Ge, Zhehao, Graf, Anton M., Keski-Rahkonen, Joonas, Slizovskiy, Sergey, Polizogopoulos, Peter, Taniguchi, Takashi, Watanabe, Kenji, Van Haren, Ryan, Lederman, David, Falko, Vladimir I., Heller, Eric J., Velasco, Jairo

Issue&Volume: 2024-11-27

Abstract: Quantum scars refer to eigenstates with enhanced probability density along unstable classical periodic orbits. First predicted 40years ago, scars are special eigenstates that counterintuitively defy ergodicity in quantum systems whose classical counterpart is chaotic. Despite the importance and long history of scars, their direct visualization in quantum systems remains an open field. Here we demonstrate that, by using an in situ graphene quantum dot (GQD) creation and a wavefunction mapping technique, quantum scars are imaged for Dirac electrons with nanometre spatial resolution and millielectronvolt energy resolution with a scanning tunnelling microscope. Specifically, we find enhanced probability densities in the form of lemniscate ∞-shaped and streak-like patterns within our stadium-shaped GQDs. Both features show equal energy interval recurrence, consistent with predictions for relativistic quantum scars. By combining classical and quantum simulations, we demonstrate that the observed patterns correspond to two unstable periodic orbits that exist in our stadium-shaped GQD, thus proving that they are both quantum scars. In addition to providing unequivocal visual evidence of quantum scarring, our work offers insight into the quantum–classical correspondence in relativistic chaotic quantum systems and paves the way to experimental investigation of other recently proposed scarring species such as perturbation-induced scars, chiral scars and antiscarring.

DOI: 10.1038/s41586-024-08190-6

Source: https://www.nature.com/articles/s41586-024-08190-6