Decoherence in Waveguide Quantum Electrodynamics using Matrix Product States

TL;DR

This paper introduces an MPS-based method for modeling decoherence in waveguide QED systems, enabling efficient simulation of loss processes like dephasing and decay in complex light-matter interactions.

Contribution

It generalizes existing MPS techniques to density matrices, allowing for the inclusion of various dissipation mechanisms in waveguide QED simulations.

Findings

Pure dephasing significantly affects light-matter interactions.

The method efficiently models off-chip radiative decay.

Different dissipation processes have qualitatively distinct impacts.

Abstract

We present a matrix product state (MPS) method for including decoherence processes in calculations involving waveguide quantum electrodynamics (waveguide QED) using density matrices. The approach is based on collision quantum optics, where the many-body state of the waveguide is represented as discrete time bins, which are efficiently represented using an MPS chain. Our method is a generalization of previous MPS methods, and we demonstrate how one can efficiently expand 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.