Multi-mode Circuit Quantum Electrodynamics with Superconducting Metamaterial Resonators

Metamaterial resonant structures made from arrays of superconducting lumped circuit elements can be used to produce novel mode spectra, in particular, a high density of modes in the same frequency range where superconducting qubits are typically operated. Such a system could have applications in quantum simulation and multipartite entanglement. We present a series of low-temperature measurements of such a superconducting metamaterial resonator coupled to a flux-tunable transmon qubit. We are able to track the qubit as we tune it through many of the metamaterial resonances using a separate conventional resonator to read out the qubit state. With this capability, we are able to map the frequency dependence of the qubit T1 time and observe structure that correlates with the metamaterial spectrum. In addition, we present time domain qubit measurements as a function of frequency in this multi-mode system as well as measurements of multi-photon two-tone experiments between qubit states and metamaterial modes.