Phase synchronization in dissipative non-Hermitian coupled quantum systems

TL;DR

This paper investigates phase synchronization in non-Hermitian quantum systems with multiple bosonic modes, deriving analytical conditions and demonstrating robustness against noise, bridging quantum dynamics and classical synchronization models.

Contribution

It introduces a fully analytical framework for phase synchronization in non-Hermitian bosonic systems, connecting quantum dynamics with the Kuramoto model.

Findings

Analytical synchronization conditions derived for bosonic modes.

Synchronization persists under external noise.

Reduction to a Kuramoto model enables known analytical solutions.

Abstract

We study the interplay between non-Hermitian dynamics and phase synchronization in a system of $\mathcal{N}$ bosonic modes coupled to an auxiliary mode. The linearity of the evolution in such a system allows for the derivation of fully analytical results for synchronization conditions. In contrast, analysis at the level of phase dynamics, followed by a transformation to a collective basis allows a complete reduction to an all-to-all coupled Kuramoto model with known analytical solutions. We provide analytical and numerical solutions for systems ranging from a few modes to the macroscopic limit of large $\mathcal{N}$ in the presence of inhomogeneous frequency broadening and test the robustness of phase synchronization under the action of external noise.