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Superconducting metamaterials are a promising resource for quantuminformation science. In the context of circuit QED, they provide a means toengineer on-chip, novel dispersion relations and a band structure that couldultimately be utilized for generating complex entangled states of quantumcircuitry, for quantum reservoir engineering, and as an element for quantumsimulation architectures. Here we report on the development and measurement atmillikelvin temperatures of a particular type of circuit metamaterial resonatorcomposed of planar superconducting lumped-element reactances in the form of adiscrete left-handed transmission line (LHTL). We discuss the details of thedesign, fabrication, and circuit properties of this system. As well, we providean extensive characterization of the dense mode spectrum in these metamaterialresonators, which we conducted using both microwave transmission measurementsand laser scanning microscopy (LSM). Results are observed to be in goodquantitative agreement with numerical simulations and also an analytical modelbased upon current-voltage relationships for a discrete transmission line. Inparticular, we demonstrate that the metamaterial mode frequencies, spatialprofiles of current and charge densities, and damping due to external loadingcan be readily modeled and understood, making this system a promising tool forfuture use in quantum circuit applications and for studies of complex quantumsystems.

Mode Structure in Superconducting Metamaterial Transmission Line Resonators