Quantum Synchronization of Twin Limit-Cycle Oscillators

TL;DR

This paper introduces a quantum Liénard system with two coexisting limit cycles, revealing unique synchronization phenomena and proposing new measures to understand quantum synchronization behavior.

Contribution

It presents a novel quantum Liénard system with dual limit cycles and explores their synchronization properties, including coexistence and blockade effects.

Findings

Coexistence of two limit cycles in a single quantum steady state.

Coupling leads to both synchronization and blockade phenomena.

Introduction of refined measures for quantum synchronization.

Abstract

Quantum synchronization has been a subject of intensive research in the last decade. In this work, we propose a quantum Li\'enard system whose classical equivalent features two limit cycles to one of which the system will converge. In the quantum case, both limit cycles coexist in a single steady state. Each of these limit cycles localizes to a distinct phase if coupled to an external drive: one quantum state can thus be assigned two phases. Furthermore, coupling two such oscillators leads to the simultaneous appearance of synchronization and a synchronization blockade. To shed light on this apparent paradoxical result, we introduce finer measures of quantum synchronization.