Topological lattices in superconducting circuit optomechanics: strained graphene model

Cavity optomechanics enables controlling mechanical motion via radiation pressure interaction, and has contributed to the quantum control of engineered mechanical systems. Yet, nearly all prior schemes have employed single- or few-mode optomechanical systems. In contrast, novel dynamics and applications are expected when utilizing optomechanical lattices. Superconducting microwave optomechanical circuits are a promising platform to implement such lattices, but have been compounded by strict scaling limitations. Here, we overcome this challenge and demonstrate topological microwave modes in 1D circuit optomechanical chains realizing the Su-Schrieffer-Heeger (SSH) model. Furthermore, we realize the strained graphene model in a 2D optomechanical honeycomb lattice. Exploiting the embedded optomechanical interaction, we show that it is possible to directly measure the mode functions of the hybridized modes without using any local probe. This enables us to reconstruct the full underlying lattice Hamiltonian and directly measure the existing residual disorder. Such optomechanical lattices, accompanied by the measurement techniques introduced, offers an avenue to explore collective, quantum many-body, and quench dynamics, topological properties and more broadly, emergent nonlinear dynamics in complex optomechanical systems with a large number of degrees of freedoms.