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We propose a scheme to simulate topological physics within a singledegenerate cavity, whose modes are mapped to lattice sites. A crucialingredient of the scheme is to construct a sharp boundary so that the openboundary condition can be implemented for this effective lattice system. Indoing so, the topological properties of the system can manifest themselves onthe edge states, which can be probed from the spectrum of an output cavityfield. We demonstrate this with two examples: a static Su-Schrieffer-Heegerchain and a periodically driven Floquet topological insulator. Our work opensup new avenues to explore exotic photonic topological phases inside a singleoptical cavity.

Dynamically manipulating topological physics and edge modes in a single degenerate optical cavity