# Synchronizing Quantum Harmonic Oscillators through Two-Level Systems

## TL;DR

This paper investigates how quantum harmonic oscillators can synchronize through their coupling with two-level systems and a reservoir, revealing the physical mechanism and generalizing the scheme to multiple oscillators and two-level systems.

## Contribution

It introduces a novel quantum synchronization scheme involving two-level systems and extends it to multiple oscillators and two-level systems.

## Key findings

- Oscillators synchronize at a single frequency with a tunable phase difference.
- The physical mechanism behind quantum synchronization is clarified.
- The scheme is generalized to multiple oscillators and two-level systems.

## Abstract

Two oscillators coupled to a two-level system which in turn is coupled to an infinite number of oscillators (reservoir) are considered, bringing to light the occurrence of synchronization. A detailed analysis clarifies the physical mechanism that forces the system to oscillate at a single frequency with a predictable and tunable phase difference. Finally, the scheme is generalized to the case of $N$ oscillators and $M(<N)$ two-level systems.