The ability to tailor with a high accuracy the intersite connectivity in a lattice is a crucial tool for realizing novel topological phases of matter. Here, we report the experimental realization of photonic dimer chains with long-range hopping terms of arbitrary strength and phase, providing a rich generalization of the Su-Schrieffer-Heeger model which, in its conventional form, is limited to nearest-neighbor couplings only. Our experiment is based on a synthetic dimension scheme involving the frequency modes of an optical fiber loop platform. This setup provides direct access to both the band dispersion and the geometry of the Bloch wave functions throughout the entire Brillouin zone allowing us to extract the winding number for any possible configuration. Finally, we highlight a topological phase transition solely driven by a time-reversal-breaking synthetic gauge field associated with the phase of the long-range hopping, providing a route for engineering topological bands in photonic lattices belonging to the AIII symmetry class.

中文翻译：

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具有长程耦合的拓扑二聚体链的波函数断层扫描

高精度定制晶格中位点间连接的能力是实现物质新拓扑相的关键工具。在这里，我们报告了具有任意强度和相位的长程跳跃项的光子二聚体链的实验实现，提供了 Su-Schrieffer-Heeger 模型的丰富泛化，该模型在其传统形式中仅限于最近邻耦合。我们的实验基于涉及光纤环路平台频率模式的合成尺寸方案。该设置可以直接访问整个布里渊区的能带色散和布洛赫波函数的几何形状，使我们能够提取任何可能配置的绕组数。最后，我们强调了仅由与长程跳跃相位相关的打破时间反转的合成规范场驱动的拓扑相变，为工程属于 AIII 对称类的光子晶格中的拓扑带提供了一条途径。