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

Topological photonics started out as a pursuit to engineer systems that mimic fermionic single-particle Hamiltonians with symmetry-protected modes, whose number 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 selectively amplified by distributed gain and loss. A key question is whether such topological mode selection persists when one accounts for the nonlinearities that stabilize these systems at their working point. Here we show that topological defect lasers can indeed stably operate in genuinely topological states. These comprise direct analogues of zero modes from the linear setting, as well as a novel class of states displaying symmetry-protected power oscillations, which appear in a spectral phase transition when the gain is increased. These effects show a remarkable practical resilience against imperfections, even if these break the underlying symmetries, and pave the way to harness the power of topological protection in nonlinear quantum devices.