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We present a detailed experimental and theoretical analysis of the dispersionand non-linear Kerr frequency shifts of plasma modes in a one-dimensionalJosephson junction chain containing 500 SQUIDs in the regime of weaknonlinearity. The measured low-power dispersion curve agrees perfectly with thetheoretical model if we take into account the Kerr renormalisation of the barefrequencies and the long-range nature of the island charge screening by aremote ground plane. We measured the self- and cross-Kerr shifts for thefrequencies of the eight lowest modes in the chain. We compare the measuredKerr coefficients with theory and find good agreement.

Kerr non-linearity in a superconducting Josephson metamaterial