On the non-Markovian quantum control dynamics

TL;DR

This paper investigates control strategies for non-Markovian quantum systems, focusing on cavity-QED setups, analyzing nonlinear dynamics, and demonstrating how measurement feedback can modulate quantum states.

Contribution

It introduces a framework for controlling non-Markovian quantum dynamics using measurement feedback, with analysis of stability and state modulation in complex cavity-QED systems.

Findings

Nonlinear equations describe time-varying decay rates in non-Markovian dynamics.

Measurement feedback via homodyne detection modulates steady quantum states.

Control influences high-dimensional quantum states and their stability.

Abstract

In this paper, we study both open-loop control and closed-loop measurement feedback control of non-Markovian quantum dynamics arising from the interaction between a quantum system and its environment. We use the widely studied cavity quantum electrodynamics (cavity-QED) system as an example, where an atom interacts with the environment composed of a collection of oscillators. In this scenario, the stochastic interactions between the atom and the environment can introduce non-Markovian characteristics into the evolution of quantum states, differing from the conventional Markovian dynamics observed in open quantum systems. As a result, the atom's decay rate to the environment varies with time and can be described by nonlinear equations. The solutions to these nonlinear equations can be analyzed in terms of the stability of a nonlinear system. Consequently, the evolution of quantum state amplitudes follows linear time-varying equations as a result of the non-Markovian quantum transient process. Additionally, by using measurement feedback through homodyne detection of the cavity output, we can modulate the steady atomic and photonic states in the non-Markovian process. When multiple coupled cavity-QED systems are involved, measurement-based feedback control can influence the dynamics of high-dimensional quantum states, as well as the resulting stable and unstable subspaces.