Heisenberg treatment of multiphoton pulses in waveguide QED with time-delayed feedback

TL;DR

This paper introduces a Heisenberg-based method to analyze non-Markovian dynamics in waveguide-QED systems with time-delayed feedback, enabling efficient and exact calculations for multiphoton pulses of arbitrary shape.

Contribution

It proposes a projection technique to decompose multi-time correlations into single-time matrix elements, facilitating numerically exact analysis of complex quantum light-matter interactions.

Findings

Allows calculation of dynamics with additional dissipation channels.

Handles multiphoton pulses of arbitrary shape.

Provides a numerically efficient and exact approach.

Abstract

The dynamics of waveguide-QED systems involving coherent time-delayed feedback give rise to a hierarchy of multi-time correlations within the Heisenberg picture due to the induced non-Markovianity. We propose to perform a projection onto a complete set of states in the Hilbert space to decompose the multi-time correlations into single-time matrix elements. To illustrate the procedure, we consider the paradigmatic example of a two-level system that couples to a semi-infinite waveguide and interacts with quantum light pulses. Our approach complements the range of available methods as it allows calculating the dynamics under the inclusion of additional dissipation channels in a numerically exact and efficient manner for multiphoton pulses of arbitrary shape where memory requirements are known in advance.