Non-Markovian Dynamics of a Qubit Due to Single-Photon Scattering in a Waveguide

TL;DR

This paper provides an exact analysis of a qubit's non-Markovian dynamics caused by single-photon scattering in waveguides, revealing unique features and sources of memory effects.

Contribution

It introduces an exact solution for the multi-photon scattering problem and characterizes the non-Markovian dynamics of the qubit with a new master equation.

Findings

Identifies non-Markovian features in qubit dynamics due to photon scattering.

Highlights the roles of photon wavepacket width and propagation delay.

Provides a rigorous framework for analyzing open quantum system dynamics.

Abstract

We investigate the open dynamics of a qubit due to scattering of a single photon in an infinite or semi-infinite waveguide. Through an exact solution of the time-dependent multi-photon scattering problem, we find the qubit's dynamical map. Tools of open quantum systems theory allow us then to discuss the general features of this map, find the corresponding non-Linbladian master equation, and assess in a rigorous way its non-Markovian nature. The qubit dynamics has distinctive features that, in particular, do not occur in emission processes. Two fundamental sources of non-Markovianity are present: the finite width of the photon wavepacket and the time delay for propagation between the qubit and the end of the semi-infinite waveguide.