Nonlinear Non-Hermitian Skin Effect and Skin Solitons in Temporal Photonic Feedback Lattices

Non-Hermitian skin effect (NHSE), i.e., the localization of eigenstates near lattice boundaries, has recently spurred tremendous interest in topological physics. Beyond the well-explored linear NHSE, the interplay of nonlinearity and skin localization represents a cutting-edge area of research, offering novel insights into wave propagation and localization control in various physical systems. Unlike the linear NHSE successfully observed in weak-power optical systems, the observation of nonlinear NHSE and resulting skin solitons remains so far elusive, mainly due to the high energy levels required in most of nonlinear effects. Here we report the experimental demonstration of nonlinear NHSE in a Kerr nonlinear temporal photonic lattice, where the high-power limitation and lack of tunability intrinsic to optical materials are overcome by an artificial nonlinearity arising from opto-electronic feedback. Thanks to Kerr self-trapping, the nonlinear NHSE is demonstrated to possess much better localization strength and robustness at the preferred boundary compared to the linear case. Away from the preferred boundary, Kerr self-trapping can even inhibit NHSE-induced transport and form stable skin solitons. Harnessing the nonlinearity-controlled NHSE, we judiciously design an optical router with a flexibly-tuned output port. Our findings promise great applications in robust signal transmission, routing, and processing.