# Mode Structure in Superconducting Metamaterial Transmission Line Resonators

## TL;DR

This paper reports on the development and detailed characterization of superconducting metamaterial resonators with a dense mode spectrum, demonstrating their potential for quantum information processing and complex quantum system studies.

## Contribution

It introduces a novel superconducting metamaterial resonator design, with comprehensive experimental and theoretical analysis of its mode structure and properties.

## Key findings

- Mode frequencies and spatial profiles match simulations and models
- Damping effects due to external loading are well understood
- Resonators show promise for quantum circuit applications

## Abstract

Superconducting metamaterials are a promising resource for quantum information science. In the context of circuit QED, they provide a means to engineer on-chip, novel dispersion relations and a band structure that could ultimately be utilized for generating complex entangled states of quantum circuitry, for quantum reservoir engineering, and as an element for quantum simulation architectures. Here we report on the development and measurement at millikelvin temperatures of a particular type of circuit metamaterial resonator composed of planar superconducting lumped-element reactances in the form of a discrete left-handed transmission line (LHTL). We discuss the details of the design, fabrication, and circuit properties of this system. As well, we provide an extensive characterization of the dense mode spectrum in these metamaterial resonators, which we conducted using both microwave transmission measurements and laser scanning microscopy (LSM). Results are observed to be in good quantitative agreement with numerical simulations and also an analytical model based upon current-voltage relationships for a discrete transmission line. In particular, we demonstrate that the metamaterial mode frequencies, spatial profiles of current and charge densities, and damping due to external loading can be readily modeled and understood, making this system a promising tool for future use in quantum circuit applications and for studies of complex quantum systems.