Nonlinearity-driven topology via spontaneous symmetry breaking

Topology and nonlinearity are deeply connected. However, whether topological effects can arise solely from the structure of nonlinear interaction terms, and the nature of the resulting topological phases, remain to large extent open questions. Here we consider a chain of parametrically driven quantum resonators coupled only via weak nearest-neighbor cross-Kerr interaction, without any quadratic tunneling term. We show that, when the drive overcomes a critical threshold value, the system undergoes a transition from the atomic limit of decoupled oscillators to a symmetry-broken topological phase. The topology is determined by the interplay of local and nearest-neighbor Kerr nonlinearities, yielding a nontrivial bulk-boundary correspondence. In the topological phase, we derive analytical approximations for the low-energy spectrum, identifying the conditions to observe topological edge modes.