Slow Light in Superconducting Metamaterial Transmission Lines with Left-Handed Dispersion

Superconducting metamaterial transmission lines composed of arrays of lumped circuit elements exhibit a left-handed dispersion relation with dense mode spectra above an infrared cutoff frequency defined by the circuit parameters. This distinctive dispersion relation leads to decreasing group velocity as a function of decreasing mode frequency. In an ideal case, the group velocity approaches zero at the infrared cutoff frequency of the left-handed device. We describe the design and characterization of an open left-handed transmission line, to which we coupled two flux-tunable transmon qubits. We quantify the delay of pulsed Gaussian wave packets as a function of mode frequency through this left-handed device, as well as the nonlinearity introduced due to the qubit interaction.