# Delayed Coherent Quantum Feedback from a Scattering Theory and a Matrix Product State Perspective

## TL;DR

This paper analyzes photon scattering in a waveguide with a mirror, providing an exact analytical solution for two-photon states and comparing it with numerical matrix product state simulations, advancing understanding of coherent quantum feedback.

## Contribution

It introduces an exact analytical approach for two-photon scattering in a feedback system and extends analysis to coherent states beyond low power, bridging theory and numerical simulations.

## Key findings

- Derived an exact resummation for two-photon scattering matrix.
- Validated analytical results with matrix product state simulations.
- Extended analysis to coherent states beyond low-power regime.

## Abstract

We study the scattering of photons propagating in a semi-infinite waveguide terminated by a mirror and interacting with a quantum emitter. This paradigm constitutes an example of coherent quantum feedback, where light emitted towards the mirror gets redirected back to the emitter. We derive an analytical solution for the scattering of two-photon states, which is based on an exact resummation of the perturbative expansion of the scattering matrix, in a regime where the time delay of the coherent feedback is comparable to the timescale of the quantum emitter's dynamics. We compare the results with numerical simulations based on matrix product state techniques simulating the full dynamics of the system, and extend the study to the scattering of coherent states beyond the low-power limit.