Qubit Dynamics in a Multi-mode Environment with a Superconducting Metamaterial Resonator

Arrays of superconducting lumped circuit elements can be used to make metamaterial resonant structures, which can exhibit novel spectra with a high density of modes in the same frequency range where superconducting qubits are typically operated. We study the dynamics of a flux-tunable transmon qubit when coupled to such a metamaterial. We measure the coupling strength of the qubit to several modes by tuning the flux bias and compare the resulting vacuum Rabi splittings with numerical and analytical models. Using a separate conventional resonator to read out the qubit state, we are able to track the qubit as we tune it through many of the metamaterial resonances. With this capability, we are able to measure the qubit T1 time as a function of frequency. We observe that T1 correlates with the metamaterial spectrum and is consistent with Purcell loss into the various modes, as described by a circuit model. In addition, we present measurements of Stark shifts of the qubit transition while driving a separate microwave tone in the vicinity of the various metamaterial modes.