To date, the concept of topological order relies heavily on the properties of single-particle bands. Only recently it has been realized that interactions can have a dramatic impact on topological properties, not only modifying the topology of the bands but also creating a topological order in an otherwise trivial system. Applying an extended version of the Bose-Hubbard model, we investigate a system which, being topologically trivial in the single-particle regime, harbors topologically nontrivial edge and interface states of repulsively bound photon pairs. Whereas binding of the photons in this model is captured by the standard local interaction term, an additional direct two-photon hopping renders the system topologically nontrivial. Besides their interaction-induced origin, predicted two-photon edge states exhibit a range of other unexpected features, including the robustness to collapse of the corresponding bulk band and the ability to coexist with the continuum of two-photon scattering states forming a bound state in the continuum. Performing rigorous calculation of the Zak phase for bound photon pairs, we prove the topological origin of the two-photon edge states.

中文翻译：

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相互作用诱导的光子对的拓扑状态

迄今为止，拓扑顺序的概念在很大程度上依赖于单粒子带的属性。直到最近，人们才意识到相互作用可以对拓扑特性产生巨大的影响，不仅可以改变谱带的拓扑结构，而且可以在其他琐碎的系统中创建拓扑顺序。应用Bose-Hubbard模型的扩展版本，我们研究了一个系统，该系统在单粒子状态下拓扑上是微不足道的，它包含排斥键合的光子对的拓扑上非平凡的边缘和界面状态。尽管此模型中的光子绑定是通过标准的局部交互作用项捕获的，但另外的直接双光子跳跃使系统在拓扑上不那么重要。除了他们的互动导致的起源，预测的双光子边缘态还表现出一系列其他不可预料的特征，包括相应的体带崩溃的鲁棒性以及与在连续体中形成束缚态的双光子散射态的连续体共存的能力。对束缚光子对执行Zak相位的严格计算，我们证明了两个光子边缘态的拓扑起源。