  Topological states of light open exciting possibilities in quantum photonics
promising the topological protection of quantum entanglement. Here, we put
forward an approach to realize the topological states of photon pairs mediated
by the effective density-dependent coupling which is manifested as the
dependence of the tunneling amplitude on the number of photons. As a specific
platform, we investigate the arrays of nearest-neighbor coupled transmon
qubits, where the effective density-dependent coupling is engineered by
inserting auxiliary frequency-detuned resonators. We prove the topological
origin of the designed model by the direct evaluation of the Zak phase
highlighting the feasibility of our proposal for state-of-the-art fabrication
technologies.
