Exciton-polariton lattices obtained by coupling electronic excitations (referred to as excitons) to the photonic modes of coupled cavities provide a platform of choice for exploring non-linear topological physics. 

I will discuss our recent progress in non-linear topological photonics using polariton lattices. I will address how we can use the Kerr non-linearity in a polariton lattice to shape topological properties of the linearized excitation spectrum: a topological edge state can be induced by a gap soliton [1] or a Thouless pump be implemented by adiabatic modification of the drive pattern [2]. Finally I will discuss how the topological classification proposed by G. Villa and collaborators [4] provides interesting insight into the complex phase diagram of two coupled Kerr resonators. We observe peculiar hysteretical behaviors, when scanning the phase between the fields driving each of the resonators [3].

[1] N. Pernet et al., Nature Physics 18, 678 (2022)

[2] S. Ravets et al., Phys. Rev. Lett. 134, 093801 (2025)

[3] Nicolas Pernet, 2022 ( https://theses.hal.science/tel-03917551 )

[4] G. Villa et al., Science Advances 11, adt9311 (2025)