We studied the transport properties of a driven-dissipative photonic network, where multiple photonic cavities are coupled through a nonreciprocal bus with unidirectional transmission. For short-range coupling between the cavities, the occurrence of nonreciprocal amplification can be linked to a topological phase transition of the underlying dynamic Hamiltonian. However, for long-range coupling, we show that the correspondence between the nonreciprocal amplification transition and the topological phase transition breaks down as the transition conditions deviate significantly from each other. We found the exact transition condition for nonreciprocal amplification, supported by analytical calculation and numerical simulation. We also investigated the stability, the crossover from short- to long-range coupling, and the bandwidth of the nonreciprocal amplification. Our work has potential applications in signal transmission and amplification, and also paves the way to study other topological and non-Hermitian systems with long-range coupling and nontrivial boundary effects.

中文翻译：

---

拓扑光子网络中的单向放大跃迁

我们研究了驱动耗散光子网络的传输特性，其中多个光子腔通过具有单向传输的非互易总线耦合。对于空腔之间的短程耦合，非互易放大的发生可以与潜在动态哈密顿量的拓扑相变相关联。然而，对于长程耦合，我们发现非互易放大跃迁与拓扑相变之间的对应关系随着跃迁条件彼此之间的显着偏离而失效。在分析计算和数值模拟的支持下，我们找到了非互易放大的确切过渡条件。我们还研究了稳定性，从短程耦合到长程耦合的交叉，和非互易放大的带宽。我们的工作在信号传输和放大方面具有潜在的应用，也为研究其他具有远程耦合和非平凡边界效应的拓扑和非厄米系统铺平了道路。