Ponente
Sr.
Eduardo Sánchez-Burillo
(Instituto de Ciencia de Materiales de Aragón (CSIC-Unizar))
Descripción
Causality is one of the most fundamental principles in physics and it has strong implications. For instance, in QFT, the scattering matrix, the mathematical object connecting input and output free states, must follow the so-called cluster-decomposition principle, which says that the scattering amplitude factorizes as a product of single-particle amplitudes for causally disconnected input states. In this work, we find that the cluster-decomposition principle also occurs in a non-causal system: the nonrelativistic scenario of waveguide QED, where a one-dimensional photonic field interacts with some scatterers. We first show a Lieb-Robinson-like bond holds for the free theory, so the system is approximately causal if there are not scatterers. We then show that the ground state of the full model is equivalent to the vacuum far away from the scattering region, so we can properly define free input and output states. We then show the Lieb-Robinson-like bond also holds for the full system. Lastly, considering that there are more stable states apart from the ground state, we show that the scattering amplitude for a bunch of causally disconnected incident photons is composed by a product of one-photon amplitudes, with a sum over all the stable states, so the cluster-decomposition principle holds. We find the structure for the S-matrix in position space compatible with this scattering amplitude. We finally illustrate our results with two examples: (i) a two-level system ultrastrongly coupled to a dispersive medium and (ii) a general scatterer coupled to a waveguide with linear dispersion relation. In the first example, we show the cluster properties hold. In the second one, we find the structure for the S-matrix in momentum space and compute how the photon-photon correlations generated by this S-matrix decay with the distance between the incident photons.
Autores primarios
Dr.
Andrea Cadarso
(Instituto de Física Fundamental, IFF-CSIC)
Dr.
David Zueco
(Universidad de Zaragoza)
Sr.
Eduardo Sánchez-Burillo
(Instituto de Ciencia de Materiales de Aragón (CSIC-Unizar))
Dr.
Juan José García-Ripoll
(CSIC - Instituto de Fisica Fundamental)
Prof.
Luis Martín-Moreno
(Instituto de Ciencia de Materiales de Aragón (CSIC-Unizar))
