# Quantum Synchronisation Enabled by Dynamical Symmetries and Dissipation

## TL;DR

This paper demonstrates that in open quantum systems, conditions involving dynamical symmetries and dissipation can guarantee robust, system-wide quantum synchronization, independent of specific parameters or initial states.

## Contribution

It introduces a general framework linking dynamical symmetries and dissipation to quantum synchronization, with explicit examples showing perfect phase-locking.

## Key findings

- Quantum systems can achieve robust synchronization through dynamical symmetries.
- Synchronization persists despite symmetry-breaking perturbations.
- Examples show perfect phase-locking in spin chains and Hubbard models.

## Abstract

In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter regime in a specific system. In this work we show that this need not be the case, identifying conditions which, when satisfied, guarantee that the individual constituents of a generic open quantum system will undergo completely synchronous limit cycles which are, to first order, robust to symmetry-breaking perturbations. We then describe how these conditions can be satisfied by the interplay between several elements: interactions, local dephasing and the presence of a strong dynamical symmetry - an operator which guarantees long-time non-stationary dynamics. These elements cause the formation of entanglement and off-diagonal long-range order which drive the synchronised response of the system. To illustrate these ideas we present two central examples: a chain of quadratically dephased spin-1s and the many-body charge-dephased Hubbard model. In both cases perfect phase-locking occurs throughout the system, regardless of the specific microscopic parameters or initial states. Furthermore, when these systems are perturbed, their non-linear responses elicit long-lived signatures of both phase and frequency-locking.

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Source: https://tomesphere.com/paper/1907.12837