Experimental robustness of quantum correlations in a Su-Schrieffer–Heeger lattice

The SSH model is a 1-D lattice model with periodically alternating coupling between the lattice sites that shows interesting topological features. We simulate the SSH model using a multimode superconducting parametric cavity. The resonance frequencies are made tunable by terminating the cavity with a SQUID, which acts as a flux-tunable inductance. 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. We observe a zero-energy edge state in a 5 site SSH lattice and two almost-zero-energy edge states in a 6 site lattice which, according to the theory, are respectively protected by the symmetry and topology of the lattice. To verify stability of the protected states, we experimentally study quantum correlations in the lattice in the presence of disorder. Creating a single-mode squeezed state at one end of the lattice, we reconstruct the quadrature covariance matrix between all sites. We test the robustness of protected states by "programming" 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.