Synchronization of persistent oscillations in spin systems with non-local dissipations

TL;DR

This paper investigates how spins in a quantum system synchronize their persistent oscillations due to non-local dissipation, revealing stable long-term behaviors and synchronization phenomena through theoretical and numerical analysis.

Contribution

It demonstrates the emergence of stable oscillations and synchronization in spin systems with non-local dissipation, including analysis of infinite-size lattices.

Findings

Stable oscillatory behaviors with purely imaginary Liouvillian eigenvalues.

Complete synchronization of next-nearest-neighbor spins.

Long-time oscillations possible in infinite lattices via cluster mean-field approximation.

Abstract

We explore the synchronization phenomenon in the quantum few-body system of spins with the non-local dissipation. Without the external driving, we find that the system can exhibit stable oscillatory behaviors in the long-time dynamics accompanied by the appearance of the purely imaginary eigenvalues of the Liouvillian. Moreover, the oscillations of the next-nearest-neighboring spins are completely synchronized revealed by the quantum trajectory analysis within the stochastic Schr\"odinger equation. The possibility of the appearance of the long-time oscillations in infinite-size lattice by means of cluster mean-field approximation is also discussed.