# Observing quantum synchronization blockade in circuit quantum electrodynamics

## TL;DR

This paper proposes a superconducting circuit setup to observe quantum synchronization blockade, demonstrating how energy quantization can prevent synchronization and revealing entanglement at finite detuning.

## Contribution

It introduces a Josephson junction circuit realization and measurement scheme for observing quantum synchronization blockade in the quantum regime.

## Key findings

- Quantum synchronization blockade can be observed in superconducting circuits.
- Entanglement occurs between oscillators at finite detuning.
- The proposed setup enables experimental investigation of quantum synchronization phenomena.

## Abstract

High quality factors, strong nonlinearities, and extensive design flexibility make superconducting circuits an ideal platform to investigate synchronization phenomena deep in the quantum regime. Recently~\cite{Loerch-2017}, it was predicted that energy quantization and conservation can block the synchronization of two identical, weakly coupled nonlinear self-oscillators. Here we propose a Josephson junction circuit realization of such a system along with a simple homodyne measurement scheme to observe this effect. We also show that at finite detuning, where phase synchronization takes place, the two oscillators are entangled in the steady state as witnessed by the positivity of the logarithmic negativity.