Microwave photonics with Josephson junction arrays: Negative refraction index and entanglement through disorder

We study different architectures for a photonic crystal in the microwave regime based on superconducting transmission lines interrupted by Josephson junctions, both in one and two dimensions. 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. Two applications are discussed in detail. In a two-dimensional structure we demonstrate the phenomenon of negative refraction. We finish by studying the creation of stationary entanglement between two superconducting qubits interacting through a disordered media.