Microwave photonics and Josephson junction arrays

We present an architecture for a photonic crystal in the microwave regime based on superconducting transmission lines interrupted by Josephson junctions. A study of the scattering properties of a single junction in the line shows that the junction behaves as a perfect mirror when the photon frequency matches the Josephson plasma frequency. We generalize our calculations to periodic arrangements of junctions, demonstrating that they can be used for tunable band engineering, forming what we call a quantum circuit crystal. As a relevant application, we discuss the creation of stationary entanglement between two superconducting qubits interacting through a disordered media.