Spin Correlations as a Probe of Quantum Synchronization in Trapped Ion Phonon-Lasers

TL;DR

This paper explores quantum synchronization in a two-ion system with non-classical phonon states, revealing correlations between spin and vibrational modes, and demonstrating how internal state measurements can indicate synchronization.

Contribution

It introduces a theoretical framework for quantum synchronization in trapped ions with few phonons, highlighting spin-vibration correlations and indirect detection methods.

Findings

Strong spin-phonon correlations within each ion

Synchronization induces correlations between ions' spins

Synchronization can be inferred from internal state measurements

Abstract

We investigate quantum synchronization theoretically in a system consisting of two cold ions in microtraps. The ions' motion is damped by a standing-wave laser whilst also being driven by a blue-detuned laser which results in self-oscillation. Working in a non-classical regime, where these oscillations contain only a few phonons and have a sub-Poissonian number variance, we explore how synchronization occurs when the two ions are weakly coupled using a probability distribution for the relative phase. We show that strong correlations arise between the spin and vibrational degrees of freedom within each ion and find that when two ions synchronize their spin degrees of freedom in turn become correlated. This allows one to indirectly infer the presence of synchronization by measuring the ions' internal state.