Modeling superconducting circuits interacting through non-standard waveguide QED topologies

Many interesting phenomena have been observed in the context of superconducting qubits strongly coupled to microwave waveguides, including directional emission, decoherence-free interactions between qubits, and generation of entangled itinerant photons. Prior work in waveguide QED typically assumes the presence of a backbone waveguide to which all qubits are connected. In this talk, we relax that assumption to model waveguide QED topologies that include waveguides interrupted with qubits, waveguide junctions, and other structures. Through analytical and numerical methods, we demonstrate a range of possible behaviors including the presence of multiple uncoupled dark state manifolds, tunable bright state decay rates, and the generation of novel photon statistics from the scattering of coherent light off these mixed waveguide-qubit systems.