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 induces 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.