We present a theoretical study of the temporal and spatial coherence properties of a topological laser device built by including saturable gain on the edge sites of a Harper-Hofstadter lattice for photons. For small enough lattices, the Bogoliubov analysis applies, and the coherence time is almost determined by the total number of photons in the device in agreement with the standard Schawlow-Townes phase diffusion. In larger lattices, looking at the lasing edge mode in the comoving frame of its chiral motion, the spatiotemporal correlations of long-wavelength fluctuations display a Kardar-Parisi-Zhang (KPZ) scaling. Still, at very long times, when the finite size of the device starts to matter, the functional form of the temporal decay of coherence changes from the KPZ stretched exponential to a Schawlow-Townes-like exponential, while the nonlinear dynamics of KPZ fluctuations remains visible as a broadened linewidth as compared to the Bogoliubov-Schawlow-Townes prediction. While we establish the above behaviors also for nontopological 1D laser arrays, the crucial role of topology in protecting the coherence from static disorder is finally highlighted: Our numerical calculations suggest the dramatically reinforced coherence properties of topological lasers compared to corresponding nontopological devices. These results open exciting possibilities for both fundamental studies of nonequilibrium statistical mechanics and concrete applications to laser devices.

中文翻译：

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拓扑激光相干理论

我们提出了一种拓扑激光设备的时空相干特性的理论研究，该设备通过在光子的Harper-Hofstadter晶格的边缘位置包括饱和增益而构建。对于足够小的晶格，可使用Bogoliubov分析，并且相干时间几乎由与标准Schawlow-Townes相扩散一致的器件中的光子总数决定。在较大的晶格中，在手征运动的同移框架中观察激光边缘模式时，长波长波动的时空相关性显示出Kardar-Parisi-Zhang（KPZ）缩放比例。不过，在很长一段时间内，当设备的有限尺寸开始起作用时，相干性时间衰减的功能形式会从KPZ拉伸指数变为类似Schawlow-Townes的指数，而与Bogoliubov-Schawlow-Townes预测相比，KPZ涨落的非线性动力学仍可以看到，但线宽变宽。虽然我们也针对非拓扑一维激光阵列建立了上述行为，但拓扑结构在保护相干免受静电干扰方面的关键作用最终得到了强调：我们的数值计算表明，与相应的非拓扑设备相比，拓扑激光器的相干特性得到了显着增强。这些结果为非平衡统计力学的基础研究和激光设备的具体应用打开了令人兴奋的可能性。最后强调了拓扑在保护相干免受静态干扰方面的关键作用：我们的数值计算表明，与相应的非拓扑设备相比，拓扑激光器的相干特性得到了显着增强。这些结果为非平衡统计力学的基础研究和激光设备的具体应用打开了令人兴奋的可能性。最后强调了拓扑在保护相干免受静态干扰方面的关键作用：我们的数值计算表明，与相应的非拓扑设备相比，拓扑激光器的相干特性得到了显着增强。这些结果为非平衡统计力学的基础研究和激光设备的具体应用打开了令人兴奋的可能性。