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Topological photonics started out as a pursuit to engineer systems that mimicfermionic single-particle Hamiltonians with symmetry-protected modes, whosenumber can only change in spectral phase transitions such as band inversions.The paradigm of topological lasing, realized in three recent experiments,offers entirely new interpretations of these states, as they can be selectivelyamplified by distributed gain and loss. A key question is whether suchtopological mode selection persists when one accounts for the nonlinearitiesthat stabilize such systems at their working point. Here we show thattopological defect lasers can indeed stably operate in genuinely topologicalstates. These comprise direct analogues of zero modes from the linear setting,as well as a novel class of states displaying symmetry-protected poweroscillations, which appear in a spectral phase transition when the gain isincreased. These effects show a remarkable practical resilience againstimperfections, even if these break the underlying symmetries, and pave the wayto harness the power of topological protection in nonlinear quantum devices.

Nonlinear mode competition and symmetry-protected power oscillations in topological lasers