Robustness of quantum correlations in topological states in Su-Schrieffer–Heeger model

Despite its simplicity, the SSH model demonstrates many interesting topological effects. Here we simulate the SSH model using a multimode superconducting parametric cavity, which is terminated by a SQUID. By applying microwave pumps to the SQUID, we activate beam-splitter interactions between cavity modes that are used as sites of the SSH lattice arrayed in synthetic dimensions. In a 5 site lattice, we observe a zero-energy edge state that theory predicts is symmetry-protected. In a 6 site lattice, we observe two almost-zero energy states localized on both edges, predicted to be topologically protected. We then experimentally study how these theoretical protections preserve the structure of quantum correlations in the lattice. Injecting a single-mode squeezed state at one site, we reconstruct the IQ covariance matrix between all sites. We test the robustness of protected states by generating ensembles with disorder in both coupling strength and site energy, observing changes in the covariance matrix. Measuring the distances between covariance matrices, we experimentally verify the improved robustness of the protected states against coupling strength disorder. Conversely, site-energy disorder, which breaks an underlying symmetry of the model, reduces the robustness.