Topological excitations and bound photon pairs in a superconducting quantum metamaterial

Recent discoveries in topological physics hold promise for disorder-robust quantum systems and technologies. Topological states provide the crucial ingredient of such systems featuring increased robustness to disorder and imperfections. Here we use an array of superconducting qubits to engineer a one-dimensional topologically nontrivial quantum metamaterial. By performing microwave spectroscopy of the fabricated array, we experimentally observe the spectrum of elementary excitations. We reveal not only the single-photon topological states but also the bands of exotic bound photon pairs arising due to the inherent anharmonicity of qubits. Furthermore, we discuss the formation of the two-photon bound edge-localized state and confirm the topological origin of our model demonstrating disorder-robust behavior of photon-photon correlation function for the topological edge state. Our work provides an experimental implementation of the topological model with attractive photon-photon interaction in a quantum metamaterial.