Role of Coherence and Degeneracies in Quantum Synchronisation

TL;DR

This paper develops a theoretical framework using Liouville space perturbation theory to understand quantum synchronisation, highlighting the roles of symmetries, coherences, and degeneracies, and linking these to thermodynamic properties.

Contribution

It introduces a novel analytical approach to quantum synchronisation, connecting spectral properties and degeneracies with thermodynamics in quantum systems.

Findings

Identifies conditions for quantum synchronisation based on eigenspectrum analysis.

Establishes a relationship between energy degeneracies and synchronisation.

Demonstrates the framework on coupled thermal machines, linking synchronisation to thermodynamics.

Abstract

Progress on the study of synchronisation in quantum systems has been largely driven by specific examples which resulted in several examples of frequency entrainment as well as mutual synchronisation. Here we study quantum synchronisation by utilising Liouville space perturbation theory. We begin by clarifying the role of centers, symmetries and oscillating coherences in the context of quantum synchronisation. We then analyse the eigenspectrum of the Liouville superoperator generating the dynamics of the quantum system and determine the conditions under which synchronisation arises. We apply our framework to derive a powerful relationship between energy conservation, degeneracies and synchronisation in quantum systems. Finally, we demonstrate our approach by analysing two mutually coupled thermal machines and the close relationship between synchronisation and thermodynamic quantities.