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Topological phases feature robust edge states that are protected against the effects of defects and disorder. These phases have largely been studied in conservatively coupled systems, in which non-trivial topological invariants arise in the energy or frequency bands of a system. Here we show that, in dissipatively coupled systems, non-trivial topological invariants can emerge purely in a system’s dissipation. Using a highly scalable and easily reconfigurable time-multiplexed photonic resonator network, we experimentally demonstrate one- and two-dimensional lattices that host robust topological edge states with isolated dissipation rates, measure a dissipation spectrum that possesses a non-trivial topological invariant, and demonst rate topological protection of the network’s quality factor. The topologically non-trivial dissipation of our system exposes new opportunities to engineer dissipation in both classical and quantum systems. Moreover, our experimental platform’s straightforward scaling to higher dimensions and its ability to implement inhomogeneous, non-reciprocal and long range couplings may enable future work in the study of synthetic dimensions.more » « less
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Abstract Topological photonics seeks to control the behaviour of the light through the design of protected topological modes in photonic structures. While this approach originated from studying the behaviour of electrons in solid-state materials, it has since blossomed into a field that is at the very forefront of the search for new topological types of matter. This can have real implications for future technologies by harnessing the robustness of topological photonics for applications in photonics devices. This roadmap surveys some of the main emerging areas of research within topological photonics, with a special attention to questions in fundamental science, which photonics is in an ideal position to address. Each section provides an overview of the current and future challenges within a part of the field, highlighting the most exciting opportunities for future research and developments.more » « less
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