Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1610.01727 · Physical Review A

Generalized cluster decomposition principle illustrated in waveguide quantum electrodynamics

Shanshan Xu, Shanhui Fan

Published Jun 9, 2017• 20 citations
arXivHTMLPDF

Abstract

We show that the form of the cluster decomposition principle, commonly used in quantum field theory, needs to be significantly generalized. As an illustration, we consider the general structure of two-photon $S$ matrix for a waveguide coupled to a local quantum system that supports multiple ground states. The presence of the multiple ground states results in a noncommutative aspect of the system with respect to the exchange of the orders of photons. Consequently, the two-photon $S$ matrix significantly differs from the standard form in quantum field theory.

DOI
10.1103/physreva.95.063809

Related papers

Theory of few-photon quantum scattering in nanophotonic structures

Shanshan Xu, Shanhui Fan

We present a generalization of the input-output formalism that provides an analytic and systematic computation tool for few-photon scattering matrix in waveguide quantum electrodynamics (QED) systems. We also discuss the theoretical constraints on such scattering matrix from the cluster decomposition principle in quantum field theory.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Feb 20, 2017•0 citations

Analytic Properties of Two-Photon Scattering Matrix in Integrated Quantum Systems Determined by the Cluster Decomposition Principle

Shanshan Xu, Eden Rephaeli, Shanhui Fan

We consider a general class of integrated quantum systems where photon-photon interaction occurs in a quantum device that is localized in space. Using techniques that are closely related to cluster decomposition principles in quantum field theory, we provide a general constraint on the analytic properties of a two-photon S matrix in this class of systems. We also show that the photon-photon interaction in these systems inevitably leads to frequency mixing and entanglement and that frequencies of the single photons cannot be preserved in these systems.

Physical Review Letters•Nov 27, 2013•73 citations

Emergent causality and theN-photon scattering matrix in waveguide QED

Eduardo Sánchez-Burillo, Andrea Cadarso, Luis Martín-Moreno +2 more

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.

arXiv:1705.09094•New Journal of Physics•Nov 27, 2017•8 citations

Cluster Decomposition and Two Senses of Isolability

Porter Williams, John Dougherty, Michael E. Miller

In the framework of quantum field theory, one finds multiple load-bearing locality and causality conditions. One of the most important is the cluster decomposition principle, which requires that scattering experiments conducted at large spatial separation have statistically independent results. The principle grounds a number of features of quantum field theory, especially the structure of scattering theory. However, the statistical independence required by cluster decomposition is in tension with the long-range correlations characteristic of entangled states. In this paper, we argue that cluster decomposition is best stated as a condition on the dynamics of a quantum field theory, not directly as a statistical independence condition. This redefinition avoids the tension with entanglement while better capturing the physical significance of cluster decomposition and the role it plays in the structure of quantum field theory.

Philosophy of Physics•Jan 1, 2024•1 citation

Implications of exceptional points for few-photon transport in waveguide quantum electrodynamics

Shanshan Xu, Shanhui Fan

We identify a general connection between the physics of exceptional points in non-Hermitian systems and the few-photon bound states in waveguide quantum electrodynamics (QED) systems. We show that, in waveguide QED systems where the local quantum system exhibits an exceptional point, the tightest-bound few-photon bound state occurs at the exceptional point. We illustrate this connection with an explicit computation on a waveguide QED system in which a waveguide is coupled to a Jaynes-Cummings system. Our result provides a quantum signature of the exceptional point physics and indicates that the physics of exceptional point can be used to understand and control the photon-photon interaction.

arXiv:1806.11279•Physical Review A•Jun 4, 2019•4 citations

Bound state of distant photons in waveguide quantum electrodynamics

A. V. Poshakinskiy, Alexander N. Poddubny

We study theoretically quantum eigenstates in an array of two-level atoms coupled to the waveguide. We show that this system features double-excited states where the two excitations are localized at the opposite edges of the array. Such bound states of distant excitations result from the long-ranged photon-mediated coupling in the waveguide setup, which mediates repulsion at larger distances. These results could be useful for the rapidly developing field of waveguide quantum electrodynamics, studying waveguide-coupled arrays of cold atoms or superconducting qubits.

arXiv:2303.09854•Physical Review A•Aug 8, 2023•5 citations
We show that the form of the cluster decomposition principle, commonly used in quantum field theory, needs to be significantly generalized. As an illustration, we consider the general structure of two-photon SSS matrix for a waveguide coupled to a local quantum system that supports multiple ground states. The presence of the multiple ground states results in a noncommutative aspect of the system with respect to the exchange of the orders of photons. Consequently, the two-photon SSS matrix significantly differs from the standard form in quantum field theory.
We consider a general class of integrated quantum systems where photon-photon interaction occurs in a quantum device that is localized in space. Using techniques that are closely related to cluster decomposition principles in quantum field theory, we provide a general constraint on the analytic properties of a two-photon S matrix in this class of systems. We also show that the photon-photon interaction in these systems inevitably leads to frequency mixing and entanglement and that frequencies of the single photons cannot be preserved in these systems.
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.
In the framework of quantum field theory, one finds multiple load-bearing locality and causality conditions. One of the most important is the cluster decomposition principle, which requires that scattering experiments conducted at large spatial separation have statistically independent results. The principle grounds a number of features of quantum field theory, especially the structure of scattering theory. However, the statistical independence required by cluster decomposition is in tension with the long-range correlations characteristic of entangled states. In this paper, we argue that cluster decomposition is best stated as a condition on the dynamics of a quantum field theory, not directly as a statistical independence condition. This redefinition avoids the tension with entanglement while better capturing the physical significance of cluster decomposition and the role it plays in the structure of quantum field theory.
We identify a general connection between the physics of exceptional points in non-Hermitian systems and the few-photon bound states in waveguide quantum electrodynamics (QED) systems. We show that, in waveguide QED systems where the local quantum system exhibits an exceptional point, the tightest-bound few-photon bound state occurs at the exceptional point. We illustrate this connection with an explicit computation on a waveguide QED system in which a waveguide is coupled to a Jaynes-Cummings system. Our result provides a quantum signature of the exceptional point physics and indicates that the physics of exceptional point can be used to understand and control the photon-photon interaction.
We study theoretically quantum eigenstates in an array of two-level atoms coupled to the waveguide. We show that this system features double-excited states where the two excitations are localized at the opposite edges of the array. Such bound states of distant excitations result from the long-ranged photon-mediated coupling in the waveguide setup, which mediates repulsion at larger distances. These results could be useful for the rapidly developing field of waveguide quantum electrodynamics, studying waveguide-coupled arrays of cold atoms or superconducting qubits.