Non-Abelian gauge fields emerge naturally in the description of adiabatically evolving quantum systems having degenerate levels. Here we show that they also play a role in Thouless pumping in the presence of degenerate bands. To this end we consider a photonic Lieb lattice having two degenerate nondispersive modes and show that, when the lattice parameters are slowly modulated, the propagation of the photons bears the fingerprints of the underlying non-Abelian gauge structure. The nondispersive character of the bands enables a high degree of control on photon propagation. Our work paves the way to the generation and detection of non-Abelian gauge fields in photonic and optical lattices.

中文翻译：

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光子晶格中的非阿贝尔 Thouless 泵浦

非阿贝尔规范场在具有简并能级的绝热演化量子系统的描述中自然出现。在这里，我们展示了在存在简并带的情况下，它们也在 Thouless 泵浦中发挥作用。为此，我们考虑具有两个简并非色散模式的光子 Lieb 晶格，并表明，当缓慢调制晶格参数时，光子的传播带有潜在非阿贝尔规范结构的指纹。带的非色散特性能够对光子传播进行高度控制。我们的工作为在光子和光学晶格中生成和检测非阿贝尔规范场铺平了道路。