Superconducting metamaterials for waveguide quantum electrodynamics. (arXiv:1802.01708v1 [quant-ph])

The embedding of tunable quantum emitters in a photonic bandgap structure
enables the control of dissipative and dispersive interactions between emitters
and their photonic bath. Operation in the transmission band, outside the gap,
allows for studying waveguide quantum electrodynamics in the slow-light regime.
Alternatively, tuning the emitter into the bandgap results in finite range
emitter-emitter interactions via bound photonic states. Here we couple a
transmon qubit to a superconducting metamaterial with a deep sub-wavelength
lattice constant ($\lambda/60$). The metamaterial is formed by periodically
loading a transmission line with compact, low loss, low disorder lumped element
microwave resonators. We probe the coherent and dissipative dynamics of the
system by measuring the Lamb shift and the change in the lifetime of the
transmon qubit. Tuning the qubit frequency in the vicinity of a band-edge with
a group index of $n_g = 450$, we observe an anomalous Lamb shift of 10 MHz
accompanied by a 24-fold enhancement in the qubit lifetime. In addition, we
demonstrate selective enhancement and inhibition of spontaneous emission of
different transmon transitions, which provide simultaneous access to long-lived
metastable qubit states and states strongly coupled to propagating waveguide

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