Stability of topologically protected edge states in nonlinear fiber loops

Abstract

We study both theoretically and experimentally the existence and stability of symmetry-protected topological chiral edge states in an all-photonic system mimicking Floquet dynamics of a discrete one-dimensional quantum walk in the presence of Kerr nonlinearity. The system is realized via time multiplexing as two fiber loops of slightly different lengths with a dynamically variable coupling strength. We prove that topological edge states persist in the nonlinear regime for moderate intensities, despite chiral symmetry breaking. Above a certain power threshold, they undergo destabilization, resulting in the radiation into the bulk modes. Finally, we show that the nonlinear interaction with bulk modes can serve as an effective pumping of the topological edge states.