  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.
