In this work we study numerically and analytically the interaction of two qubits in a one-dimensional waveguide, as mediated by the photons that propagate through the guide. We develop strategies to assert the Markovianity of the problem, the effecti
ve qubit-qubit interactions and their individual and collective spontaneous emission. We prove the existence of collective Lamb-shifts that affect the qubit-qubit interactions and the dependency of coherent and incoherent interactions on the qubit separation. We also develop the scattering theory associated to these models and prove single photon spectroscopy does probes the renormalized resonances of the single- and multi-qubit models, in sharp contrast with earlier toy models where individual and collective Lamb shifts cancel.
Based on a circuit QED qubit-cavity array a source of two-mode entangled microwave radiation is designed. Our scheme is rooted in the combination of external driving, collective phenomena and dissipation. On top of that the reflexion symmetry is brok
en via external driving permitting the appearance of chiral emission. Our findings go beyond the applications and are relevant for fundamental physics, since we show how to implement quantum lattice models exhibiting criticality driven by dissipation.
