Embedding of Time-Delayed Quantum Feedback in a Nonreciprocal Array

TL;DR

This paper introduces a novel method to encode time-delayed quantum feedback into a nonreciprocal oscillator chain, transforming a non-Markovian system into a Markovian one for easier analysis and control.

Contribution

The authors present a new approach to implement and analyze time-delayed quantum feedback using nonreciprocal auxiliary oscillators, enabling efficient treatment of complex quantum systems.

Findings

Successfully embedded non-Markovian feedback into a Markovian framework

Enhanced tunability of quantum feedback systems

Applied method to a driven-dissipative atom in front of a mirror

Abstract

Time-delayed quantum feedback is a fast and efficient method to control and stabilize few and many-body quantum systems. However, a proper understanding of such systems stays opaque due to the non-Markovian nature of the feedback protocol. Here, we present a method of encoding time-delayed quantum feedback into a chain of nonreciprocally coupled auxiliary oscillators. Our approach serves as a novel method of introducing time-delayed quantum feedback and provides the advantage of large tunability. Importantly, within our approach the original non-Markovian system is embedded into an enlarged Markovian open quantum system, which can be treated efficiently with quantum many-body methods. As an exemplary illustration, we apply our Markovian embedding approach to the paradigmatic case of a driven-dissipative atom in front of a mirror.