Dissipative and dispersive dynamics of a transmon qubit in a superconducting metamaterial

The coupling of tunable quantum emitters to a microwave photonic crystal enables the control of dissipative and dispersive interactions between qubits and their photonic bath. Operation in the transmission band allows for studying waveguide quantum electrodynamics (QED) in the slowlight regime. Alternatively, tuning the qubits into the bandgap results in finite range qubit-qubit interactions via localized photonic states. We couple a transmon qubit to a superconductive metamaterial formed by periodically loading a transmission line with lumped element microwave resonators. We probe the coherent and dissipative dynamics of the system by measuring the Lamb shift and lifetime of the qubit, respectively. In addition, we demonstrate selective enhancement and inhibition of spontaneous emission of different transmon transitions. This approach enables simultaneous access to long-lived metastable qubit states as well as short-lived states strongly coupled to waveguide modes.