A superconducting metamaterials transmission line resonator: experimental verification of the non-uniform mode spacing

Superconducting transmission line resonators (TLRs) have been widely applied to circuit quantum electrodynamical systems for superconducting quantum computation and single-photon detections. Recently, such a right-handed TLR has been generalized to electromagnetic metamaterials (MTMs), and its unconventional mode structure has been experimentally characterized [H. Wang et al., Phys. Rev. Applied 11, 054062 (2019)]. Here, we demonstrate another kind of MTM TLR, a superconducting quarter-wavelength composite right/left-handed (CRLH) TLR composed of lumped-elements. We design the devices and analyze their transport properties by developing a real-space approach, wherein the physical parameters at the device boundaries are utilized conveniently. Superconducting MTM TLRs with typical three unit cells were experimentally prepared by etching a superconducting aluminum film on a SiO2 substrate, and their microwave transport properties were measured at low temperatures of 50mK. The results show that the modes spacing in such a quarter-wavelength CRLH-TLR is non-uniform due to the nonlinear dispersion relation. This implies that they could be utilized to encode the superconducting qubits, analogously to the usual ones encoded by the Josephson devices.