000069661 001__ 69661 000069661 005__ 20191212100702.0 000069661 0247_ $$2doi$$a10.1088/1367-2630/aa9cc2 000069661 0248_ $$2sideral$$a104631 000069661 037__ $$aART-2018-104631 000069661 041__ $$aeng 000069661 100__ $$0(orcid)0000-0002-3230-5824$$aSánchez-Burillo, E. 000069661 245__ $$aEmergent causality and the N-photon scattering matrix in waveguide QED 000069661 260__ $$c2018 000069661 5060_ $$aAccess copy available to the general public$$fUnrestricted 000069661 5203_ $$aIn this work we discuss the emergence of approximate causality in a general setup from waveguide QED - i.e. a one-dimensional propagating field interacting with a scatterer. We prove that this emergent causality translates into a structure for the N-photon scattering matrix. Our work builds on the derivation of a Lieb-Robinson-type bound for continuous models and for all coupling strengths, as well as on several intermediate results, of which we highlight: (i) the asymptotic independence of space-like separated wave packets, (ii) the proper definition of input and output scattering states, and (iii) the characterization of the ground state and correlations in the model. We illustrate our formal results by analyzing the two-photon scattering from a quantum impurity in the ultrastrong coupling regime, verifying the cluster decomposition and ground-state nature. Besides, we generalize the cluster decomposition if inelastic or Raman scattering occurs, finding the structure of the -matrix in momentum space for linear dispersion relations. In this case, we compute the decay of the fluorescence (photon-photon correlations) caused by this S-matrix. 000069661 536__ $$9info:eu-repo/grantAgreement/ES/CAM/QUITEMAD-S2013-ICE-2801$$9info:eu-repo/grantAgreement/ES/DGA/FENOL-GROUP$$9info:eu-repo/grantAgreement/ES/MINECO/FIS2015-70856-P$$9info:eu-repo/grantAgreement/ES/MINECO/MAT2014-53432-C5-1-R 000069661 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000069661 590__ $$a3.773$$b2018 000069661 591__ $$aPHYSICS, MULTIDISCIPLINARY$$b12 / 81 = 0.148$$c2018$$dQ1$$eT1 000069661 592__ $$a1.664$$b2018 000069661 593__ $$aPhysics and Astronomy (miscellaneous)$$c2018$$dQ1 000069661 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000069661 700__ $$aCadarso, A. 000069661 700__ $$0(orcid)0000-0001-9273-8165$$aMartín-Moreno, L.$$uUniversidad de Zaragoza 000069661 700__ $$aGarcía-Ripoll, J.J. 000069661 700__ $$0(orcid)0000-0003-4478-1948$$aZueco, D.$$uUniversidad de Zaragoza 000069661 7102_ $$12003$$2395$$aUniversidad de Zaragoza$$bDpto. Física Materia Condensa.$$cÁrea Física Materia Condensada 000069661 773__ $$g20, 1 (2018), 013017 [20 pp]$$pNew j. phys.$$tNEW JOURNAL OF PHYSICS$$x1367-2630 000069661 8564_ $$s746988$$uhttps://zaguan.unizar.es/record/69661/files/texto_completo.pdf$$yVersión publicada 000069661 8564_ $$s12019$$uhttps://zaguan.unizar.es/record/69661/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000069661 909CO $$ooai:zaguan.unizar.es:69661$$particulos$$pdriver 000069661 951__ $$a2019-12-12-10:04:46 000069661 980__ $$aARTICLE