Driven-dissipative fermionized topological phases of strongly interacting bosons

We study the optical response of a one-dimensional array of strongly nonlinear optical microcavities with alternating tunnel transmissivities, mimicking the paradigmatic Su-Schriefer Heeger model. We show that the non-equilibrium steady state of the bosonic system contains clear signatures of fermionization when the intra-cavity Kerr non-linearity is stronger than both losses and inter-site tunnel coupling. Furthermore, by changing the experimentally controllable parameters detuning and driving strength, in a topologically non-trivial phase, one can selectively excite either the bulk or edge modes or both modes, revealing interesting topological properties in a non-equilibrium system.