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  • Open Access

Decoherence in waveguide quantum electrodynamics using matrix product states

Matias Bundgaard-Nielsen1,2,*, Matthew Kozma3, Sofia Arranz Regidor3, and Stephen Hughes3

  • *Contact author: matbu@dtu.dk
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Phys. Rev. Research 8, 033109 – Published 27 July, 2026

DOI: https://doi.org/10.1103/fmpt-dp44

Abstract

We present a matrix product state (MPS) method for including decoherence processes in calculations involving waveguide quantum electrodynamics (QED) using density matrices. The approach is based on collision quantum optics, where the many-body state of the waveguide is represented using discrete time bins, which are then efficiently encoded using an MPS chain. Our method is a generalization of previous MPS methods, and we demonstrate how one can efficiently extend the method to density matrices, allowing for the inclusion of various loss processes in the form of Lindblad terms in the Liouvillian superoperator responsible for the relevant dissipation dynamics. As an application of the theory, we study various waveguide QED systems and the influence of emitter pure dephasing (which is one of the most important processes in real systems) on the light-matter interactions, including a two-level system (TLS) in a semi-infinite waveguide with time-delayed feedback, two spatially separated TLSs with finite delays, and finally the scattering of few-photon Fock pulses on a TLS. In addition to emitter pure dephasing, we also show how to include off-chip radiative decay, and show how it differs qualitatively from pure dephasing.

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Phys. Rev. Research 8, 033109– Published 27 July, 2026
  • Received 20 April 2026
  • Accepted 1 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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