Waveguide-QED with one-dimensional Josephson metamaterials

Quantum emitters coupled to waveguides constitute one of the paradigmatic platforms for the implementation of quantum technologies based on collective qubit-photon interactions, such as remote entanglement generation, quantum metrology, and quantum communication. Interestingly, the properties of the emission spectrum are completely determined by the nature of coupling to the waveguide and its dispersion relation, independent of the details of the emitter. Here we study the collective dynamics of a system consisting of a left-handed Josephson transmission line (LJTL) strongly coupled to a superconducting qubit. Interestingly, we find that the LJTL implements an engineered reservoir with an asymmetric spectral function, leading to fractional decay of qubit population and therefore to qubit-photon bound-states outside the continuum. We explore the modification of photon emission due to the nonlinearity of the reservoir and the extension of these ideas to systems with multiple qubits.