Photon-mediated qubit interactions in one-dimensional discrete and continuous models

11 págs.; 9 figs.; 1 app.; PACS number(s): 42.50.Pq, 42.50.Gy, 32.80.−t, 85.25.Cp© 2015 American Physical Society. 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 effective 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 with these models and prove single-photon spectroscopy does probe the renormalized resonances of the single- and multiqubit models, in sharp contrast to earlier toy models in which individual and collective Lamb shifts cancel.The authors acknowledge support from Spanish Mineco project FIS2012-33022, CAM Research Consortium QUITEMAD+ (S2013/ICE-2801), EU Marie Curie C.I.G. 630955 NewFQS, and EU FP7 FET-Open project PROMISCE. J.J.G.R. acknowledges computer resources and assistance provided by the Centro de Supercomputacion y Visualizacion de Madrid (CeSViMa) and the Spanish Supercomputing NetworkPeer Reviewe