Emergent causality and the N-photon scattering matrix in waveguide QED
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 de...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2018-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/aa9cc2 |
| _version_ | 1827873490530729984 |
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| author | E Sánchez-Burillo A Cadarso L Martín-Moreno J J García-Ripoll D Zueco |
| author_facet | E Sánchez-Burillo A Cadarso L Martín-Moreno J J García-Ripoll D Zueco |
| author_sort | E Sánchez-Burillo |
| collection | DOAJ |
| description | 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 $S$ -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. |
| first_indexed | 2024-03-12T16:37:47Z |
| format | Article |
| id | doaj.art-b7968b3f79d74ef6996c290c28a0c99b |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:37:47Z |
| publishDate | 2018-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-b7968b3f79d74ef6996c290c28a0c99b2023-08-08T14:49:01ZengIOP PublishingNew Journal of Physics1367-26302018-01-0120101301710.1088/1367-2630/aa9cc2Emergent causality and the N-photon scattering matrix in waveguide QEDE Sánchez-Burillo0A Cadarso1L Martín-Moreno2J J García-Ripoll3https://orcid.org/0000-0001-8993-4624D Zueco4Instituto de Ciencia de Materiales de Aragón and Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza , E-50009 Zaragoza, SpainInstituto de Física Fundamental , IFF-CSIC, Calle Serrano 113b, Madrid E-28006, SpainInstituto de Ciencia de Materiales de Aragón and Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza , E-50009 Zaragoza, SpainInstituto de Física Fundamental , IFF-CSIC, Calle Serrano 113b, Madrid E-28006, SpainInstituto de Ciencia de Materiales de Aragón and Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza , E-50009 Zaragoza, Spain; Fundación ARAID , Paseo María Agustín 36, E-50004 Zaragoza, SpainIn 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 $S$ -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.https://doi.org/10.1088/1367-2630/aa9cc2waveguide QEDcausalityscattering matrixcluster-decomposition principle |
| spellingShingle | E Sánchez-Burillo A Cadarso L Martín-Moreno J J García-Ripoll D Zueco Emergent causality and the N-photon scattering matrix in waveguide QED New Journal of Physics waveguide QED causality scattering matrix cluster-decomposition principle |
| title | Emergent causality and the N-photon scattering matrix in waveguide QED |
| title_full | Emergent causality and the N-photon scattering matrix in waveguide QED |
| title_fullStr | Emergent causality and the N-photon scattering matrix in waveguide QED |
| title_full_unstemmed | Emergent causality and the N-photon scattering matrix in waveguide QED |
| title_short | Emergent causality and the N-photon scattering matrix in waveguide QED |
| title_sort | emergent causality and the n photon scattering matrix in waveguide qed |
| topic | waveguide QED causality scattering matrix cluster-decomposition principle |
| url | https://doi.org/10.1088/1367-2630/aa9cc2 |
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