Temporary Researcher Alessandro Coppo

Topological phase induced by Kerr non-linearities in spontaneously symmetry broken quantum resonators

In this talk we show that cross-Kerr non-linearities can induce topological phases and edge states in an otherwise topologically trivial system. In particular, we consider a chain of parametrically-driven quantum resonators, with local Kerr and nearest-neighbour cross-Kerr non-linearities. We study the limit in which the non-linearities are vanishingly small and the system undergoes a second-order critical phase transition. When the parametric drive is below threshold, all Kerr terms can be neglected, the resonators are effectively decoupled, and the low-energy spectrum is given by local squeezed Fock states. On the contrary, when the drive overcomes a critical value, the system enters a spontaneously symmetry broken regime, the growth of excitations makes non-linear contributions unavoidably relevant, and the Kerr terms play a key role for the stabilization of the system. Using Gaussian expansions around semi-classical equilibrium points, we find different effective models for periodic (bulk) and open (edge) boundary conditions. We then analytically derive approximate solutions for the low-energy spectrum beyond threshold and show how staggered cross-Kerr terms induce a non-trivial Zak phase associated with topological edge states at the boundary.