Topology with memory in nonlinear driven-dissipative photonic lattices

We consider a photonic lattice of nonlinear lossy resonators subjected to a coherent drive, where the system remembers its topological phase. Initially, the system is topologically trivial. After the application of an additional coherent pulse, the intensity is increased, which modifies the couplings in the system and then induce a topological phase transition. However, when the effect of the pulse dies out, the system does not go back to the trivial phase. Instead, it remembers the topological phase and maintains its topology acquired during the pulse application. The pulse can be used as a switch to trigger amplification of the topological modes. We further show that the amplification takes place at a different frequency as well as at a different position from those of the pulse, indicating frequency conversion and intensity transfer. Our work can be useful in triggering the different functionalities of active topological photonic devices.