Kerr effect in a non-linear superconducting Josephson metamaterial

We present a detailed experimental and theoretical analysis of the dispersion and Kerr frequency shifts of plasma modes in a one-dimensional Josephson junction chain containing 500 SQUIDs in the regime of weak nonlinearity. The measured low-power dispersion curve agrees perfectly with the theoretical model if we take into account the Kerr renormalisation of the bare frequencies and long-range Coulomb interaction between island charges due to a remote ground plane. We measured the self- and cross-Kerr shifts for the frequencies of the eight lowest modes in the chain. We compare the measured Kerr coefficients with theory and find fairly good agreement.