Abstract
In 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.
Highlights
Causality is expected to hold in every circumstance
In quantum field theory (QFT), strict causality imposes that two operators A(x, t ) and B (y, t¢) acting on two space-like separated points (x, t) and (y, t¢), must commute
In this work we demonstrate the existence and explore the consequences of emergent causality in the nonrelativistic framework of waveguide QED [9,10,11,12,13]
Summary
E Sánchez-Burillo, A Cadarso, L Martín-Moreno, J J García-Ripoll and D Zueco.
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