Quantum chaos, equilibration and control in extremely short spin chains

TL;DR

This paper investigates how small, three-spin quantum chains can exhibit chaotic behavior and internal equilibration, revealing that quantum chaos influences control even in minimal systems, with implications for quantum control experiments.

Contribution

It demonstrates that even extremely short spin chains can display chaotic dynamics and internal equilibration, challenging the notion that large systems are necessary for quantum chaos.

Findings

Three-spin chains can reproduce the integrable to chaos transition.

Chaotic behavior can be detected via purity degradation of a single spin.

Quantum chaos limits the degree of control achievable in small quantum systems.

Abstract

The environment of an open quantum system is usually modelled as a large many-body quantum system. However, when an isolated quantum system itself is a many-body quantum system, the question of how large and complex it must be in order to generate internal equilibration is an open key-point in the literature. In this work, by monitoring the degree of equilibration of a single spin through its purity degradation, we are able to sense the chaotic behaviour of the generic spin chain to which it is coupled. Quite remarkably, this holds even in the case of extremely short spin chains composed of three spins, where we can also reproduce the whole integrable to chaos transition. Finally, we discuss implications on quantum control experiments and show that quantum chaos reigns over the best degree of control achieved, even in small chains.