Indirect control of the asymptotic states of a quantum dynamical semigroup

TL;DR

This paper investigates how indirect control via an auxiliary system can modify the long-term behavior of open quantum systems, even with purely dissipative coupling, turning environmental effects into a control resource.

Contribution

It demonstrates that the asymptotic states of quantum dynamical semigroups can be altered through indirect control, providing necessary conditions and physical examples for this process.

Findings

Asymptotic states can be modified via indirect control.

Purely dissipative coupling does not prevent control of the asymptotic state.

Environmental interactions can be harnessed for control purposes.

Abstract

In the dynamics of open quantum systems, the interaction with the external environment usually leads to a contraction of the set of reachable states for the system as time increases, eventually shrinking to a single stationary point. In this contribution we describe to what extent it is possible to modify this asymptotic state by means of indirect control, that is by using an auxiliary system coupled to the target system in order to affect its dynamics, when there is a purely dissipative coupling between the two systems. We prove that, also in this restrictive case, it is possible to modify the asymptotic state of the relevant system, give necessary conditions for that and provide physical examples. Therefore, in indirect control schemes, the environmental action has not only a negative impact on the dynamics of a system, it is rather possible to make use of it for control purposes.