Understanding synchronization between quantum self-sustained oscillators through coherence generation

TL;DR

This paper investigates the mechanisms of quantum phase synchronization across different systems, identifying key coherence resources and providing a unified theoretical framework validated by known models.

Contribution

It introduces a general condition on the joint density matrix elements necessary for quantum phase synchronization, applicable to various quantum systems.

Findings

Identifies coherence elements as resources for synchronization

Derives a simple condition for phase distribution contribution

Validates theory with known interaction models

Abstract

Understanding the origin of phase synchronization between quantum self-sustained oscillators has garnered significant interest in recent years. In this work, we study phase synchronization in three settings: between two continuous-variable oscillators, between two arbitrary quantum spins, and within a hybrid setup involving a spin and an oscillator. We derive a simple and general condition on the elements of the joint density matrix that must be satisfied for them to contribute to the relative phase distribution. In particular, we identify the subset of coherence elements in the joint density matrix that serve as key resources for enabling quantum phase synchronization. Our theory is validated against the previously proposed interaction models known to induce synchronization between the self-sustained oscillators. Moreover, our approach offers valuable insights into the relationship between phase synchronization and various information-theoretic measures.