Dynamics of Many-Body Quantum Synchronisation

TL;DR

This paper investigates the transition to synchronization in a many-body quantum system of coupled quantum van der Pol oscillators, revealing unique quantum uncertainty features and transient dynamics near the critical coupling.

Contribution

It introduces a self-consistent mean-field analysis of quantum synchronization, highlighting the role of quantum uncertainties and transient states in many-body systems.

Findings

Synchronization occurs above a critical coupling strength.

Synchronized states exhibit lower phase and higher number uncertainties.

Transient synchronized states decay with a critical scaling law.

Abstract

We analyse the properties of the synchronisation transition in a many-body system consisting of quantum van der Pol oscillators with all-to-all coupling using a self-consistent mean-field method. We find that the synchronised state, which the system can access for oscillator couplings above a critical value, is characterised not just by a lower phase uncertainty than the corresponding unsynchronised state, but also a higher number uncertainty. Just below the critical coupling the system can evolve to the unsynchronised steady state via a long-lived transient synchronised state. We investigate the way in which this transient state eventually decays and show that the critical scaling of its lifetime is consistent with a simple classical model.