论文标题
提取非亚洲量子公制张量及其相关的Chern数字
Extracting non-Abelian quantum metric tensor and its related Chern numbers
论文作者
论文摘要
参数空间中量子状态的完整几何形状以量子几何张量为特征，量子几何张量分别包含量子指标和浆果曲率作为真实和虚构部分。当量子状态退化时，量子度量标准和浆果曲率采用非亚伯式形式。已经测量了非阿布尔（Abelian）浆果曲率和Abelian量子公制。但是，仍然缺乏一种实验可行的方案，以提取非亚伯量子公制张量的所有组件。在这里，我们提出了一项通用协议，以根据测量参数淬灭后的过渡概率，在任何维参数空间中直接在任意退化量子状态下以任意退化量子状态提取非亚洲量子度量标准张量。此外，我们表明可以测量非亚伯量子指标，以获得广义的狄拉克单子的真实Chern数和Yang单极的第二个Chern数，可以分别在人工量子系统的三维和五维参数空间中模拟。我们还证明了我们对这两种应用具有数值模拟的应用程序的可行性。
The complete geometry of quantum states in parameter space is characterized by the quantum geometric tensor, which contains the quantum metric and Berry curvature as the real and imaginary parts, respectively. When the quantum states are degenerate, the quantum metric and Berry curvature take non-Abelian forms. The non-Abelian (Abelian) Berry curvature and Abelian quantum metric have been experimentally measured. However, an experimentally feasible scheme to extract all the components of the non-Abelian quantum metric tensor is still lacking. Here we propose a generic protocol to directly extract the non-Abelian quantum metric tensor in arbitrary degenerate quantum states in any dimensional parameter space, based on measuring the transition probabilities after parameter quenches. Furthermore, we show that the non-Abelian quantum metric can be measured to obtain the real Chern number of a generalized Dirac monopole and the second Chern number of a Yang monopole, which can be simulated in three and five-dimensional parameter space of artificial quantum systems, respectively. We also demonstrate the feasibility of our quench scheme for these two applications with numerical simulations.
