Unraveling coherent quantum feedback for Pyragas control

TL;DR

This paper introduces a Heisenberg operator framework for coherent quantum feedback and Pyragas control, enabling efficient dynamics calculation and detailed analysis of entanglement growth and non-Markovian correlations in quantum systems.

Contribution

It presents a novel, easy-to-implement model that unravels quantum kinetics and is compatible with common approximation schemes for diverse quantum setups.

Findings

Efficient calculation of feedback-driven observable dynamics.

Explicit analysis of entanglement growth and non-Markovian correlations.

Applicability to both closed and open quantum systems with Pyragas control.

Abstract

We present a Heisenberg operator based formulation of coherent quantum feedback and Pyragas control. This model is easy to implement and allows for an efficient and fast calculation of the dynamics of feedback-driven observables as the number of contributing correlations grows in systems with a fixed number of excitations only linearly in time. Furthermore, our model unravels the quantum kinetics of entanglement growth in the system by explicitly calculating non-Markovian multi-time correlations, e.g., how the emission of a photon is correlated with an absorption process in the past. Therefore, the time-delayed differential equations are expressed in terms of insightful physical quantities. Another considerate advantage of this method is its compatibility to typical approximation schemes, such as factorization techniques and the semi-classical treatment of coherent fields. This allows the application on a variety of setups, ranging from closed quantum systems in the few excitation regimes to open systems and Pyragas control in general.