基于量子度规的阿贝尔规范场非阿贝尔几何相位的优化设计策略
Optimal design strategy for non-Abelian geometric phases using Abelian gauge fields based on quantum metric
摘要：
在量子力学中普遍存在的几何相位通常不仅仅是标量。事实上，它们通常是与非阿贝尔几何相关联的矩阵值对象。在这里，我们展示了如何广义，非阿贝尔几何相位可以实现使用电磁波通过耦合光子波导结构。波导实现了一个有效的哈密顿量拥有一个退化的暗子空间，其中可以发生绝热演化。相关的量子度规引出了定义最佳绝热演化的测地线的概念。用威尔逊圈研究了阿贝尔规范场的非阿贝尔演化。
英文摘要：
Geometric phases, which are ubiquitous in quantum mechanics, are commonly more than only scalar quantities. Indeed, often they are matrix-valued objects that are connected with non-Abelian geometries. Here we show how generalized, non-Abelian geometric phases can be realized using electromagnetic waves travelling through coupled photonic waveguide structures. The waveguides implement an effective Hamiltonian possessing a degenerate dark subspace, in which an adiabatic evolution can occur. The associated quantum metric induces the notion of a geodesic that defines the optimal adiabatic evolution. We exemplify the non-Abelian evolution of an Abelian gauge field by a Wilson loop.
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