Optimal control of many-body quantum dynamics: chaos and complexity

TL;DR

This paper explores how the complexity and chaotic properties of many-body quantum systems influence their controllability, using optimal control theory to derive control fields for spin chains and analyzing their spectral properties.

Contribution

It demonstrates that system complexity affects control field spectral complexity, while chaos does not significantly impact controllability in many-body quantum systems.

Findings

Spectral bandwidth of control fields is independent of system size.

Spectral complexity of control fields increases with the number of particles.

System chaos does not significantly hinder controllability.

Abstract

Achieving full control of the time-evolution of a many-body quantum system is currently a major goal in physics. In this work we investigate the different ways in which the controllability of a quantum system can be influenced by its complexity, or even its chaotic properties. By using optimal control theory, we are able to derive the control fields necessary to drive various physical processes in a spin chain. Then, we study the spectral properties of such fields and how they relate to different aspects of the system complexity. We find that the spectral bandwidth of the fields is, quite generally, independent of the system dimension. Conversely, the spectral complexity of such fields does increase with the number of particles. Nevertheless, we find that the regular o chaotic nature of the system does not affect signficantly its controllability.