# Quantum Synchronization Blockade: Energy Quantization hinders Synchronization of Identical Oscillators

## TL;DR

In the quantum regime, energy quantization prevents identical oscillators from synchronizing, and detuning can actually promote synchronization, contrasting classical expectations.

## Contribution

This paper introduces the concept of quantum synchronization blockade, showing how energy quantization inhibits synchronization of identical oscillators.

## Key findings

- Quantum synchronization blockade demonstrated in Kerr-type oscillators
- Detuning can enhance synchronization in the quantum regime
- Proposed implementations with superconducting circuits and trapped ions

## Abstract

Classically, the tendency towards spontaneous synchronization is strongest if the natural frequencies of the self-oscillators are as close as possible. We show that this wisdom fails in the deep quantum regime, where the uncertainty of amplitude narrows down to the level of single quanta. Under these circumstances identical self-oscillators cannot synchronize and detuning their frequencies can actually help synchronization. The effect can be understood in a simple picture: Interaction requires an exchange of energy. In the quantum regime, the possible quanta of energy are discrete. If the extractable energy of one oscillator does not exactly match the amount the second oscillator may absorb, interaction, and thereby synchronization is blocked. We demon- strate this effect, which we coin quantum synchronization blockade, in the minimal example of two Kerr-type self-oscillators and predict consequences for small oscillator networks, where synchronization between blocked oscillators can be mediated via a detuned oscillator. We also propose concrete implementations with super- conducting circuits and trapped ions. This paves the way for investigations of new quantum synchronization phenomena in oscillator networks both theoretically and experimentally.