Microwave propagation and localization in modulated ultralong Josephson junction chains.

A linear homogeneous chain of Josephson tunnel junctions supports TEM wave (microwave) propagation. Furthermore, these waves interact with each other due to the Josephson non-linearity. We have fabricated ultralong chains containing over 30,000 junctions with lithographically-modulated junction areas. Thanks to the large Josephson kinetic inductance, the chains have a high wave impedance (about 10 kΩ) and a low speed of light (lower than c/100), yielding wavelength much smaller than the system size. Periodic modulation results in gaps in the spectrum whose position and width can be controlled by fabrication. Such a system realizes intriguing interacting photonic crystals. Random modulation is predicted to result in the frequency-dependent Anderson localization of light, which also becomes particularly interesting in the presence of interactions. We report our spectroscopic measurements of modulated chains and discuss the interplay between dispersion, disorder, interaction, and dissipation. We also characterize spatial disorder in nominally homogeneous chains, which is important for understanding reproducible junction fabricaition.