Metamaterial Slow-Light Waveguide for Finite Range Interactions and Non-Markovian Dynamics with Superconducting Qubits

The ability to engineer the dispersion of light through subwavelength patterning of bulk materials has been a powerful tool for studying the influence of novel electromagnetic environments on light-matter interactions. Here, we present the experimental realization of an on-chip superconducting metamaterial waveguide composed of an array of coupled resonators of subwavelength size and negligible frequency disorder. By matching the array boundaries to 50Ω coplanar waveguides, our design achieves an 80MHz bandwidth photonic channel with nearly constant group index of ~650, as well as extinction of more than 70dB outside of the passband. Coupling transmon qubits to this metamaterial allows us to study non-Markovian dynamics of a single qubit’s interaction with the photonic bath, as well as collective non-Markovian dynamics of multiple qubits. Moreover, far from the passband, we can dynamically measure finite-range qubit-qubit interactions that extend beyond nearest neighbor and depend on detuning from the bandedge. We thus establish our metamaterial design as an attractive platform for studying photon-mediated non-Markovian dynamics and quantum many-body physics.