Quantum spin van der Pol oscillator -- a spin-based limit-cycle oscillator exhibiting quantum synchronization

TL;DR

This paper introduces a quantum spin van der Pol oscillator model that demonstrates quantum synchronization phenomena, including entrainment and entanglement, across different coupling configurations, bridging quantum optics and spin systems.

Contribution

It presents a novel spin-based limit-cycle oscillator model that generalizes quantum optical vdP oscillators to finite spins, enabling analysis of quantum synchronization in spin systems.

Findings

Demonstrates frequency entrainment to periodic drive.

Shows mutual and collective synchronization in coupled spins.

Reveals entanglement tongues in dissipatively coupled spins.

Abstract

We introduce a quantum spin van der Pol (vdP) oscillator as a prototypical model of quantum spinbased limit-cycle oscillators, which coincides with the quantum optical vdP oscillator in the high-spin limit. The system is described as a noisy limit-cycle oscillator in the semiclassical regime at large spin numbers, exhibiting frequency entrainment to a periodic drive. Even in the smallest spin-1 case, mutual synchronization, Arnold tongues, and entanglement tongues in two dissipatively coupled oscillators, and collective synchronization in all-to-all coupled oscillators are clearly observed. The proposed quantum spin vdP oscillator will provide a useful platform for analyzing quantum spin synchronization.