Seeding crystallization in time

TL;DR

This paper explores how a single time crystal can induce synchronized time-translation symmetry breaking across an ensemble, revealing that weaker coupling suffices for synchronization in more detuned systems due to seeding effects.

Contribution

It introduces the concept of seeding in time crystals, demonstrating how a single broken-symmetry subsystem can induce symmetry breaking throughout an ensemble, and uncovers novel synchronization behavior.

Findings

Seeding can induce time-translation symmetry breaking across the ensemble.

Weaker coupling is needed for synchronization in more detuned time crystals.

Seeding explains the counterintuitive synchronization behavior observed.

Abstract

We introduce the concept of seeding of crystallization in time by studying the dynamics of an ensemble of coupled continuous time crystals. We demonstrate that a single subsystem in a broken-symmetry phase acting as a nucleation center may induce time-translation symmetry breaking across the entire ensemble. Seeding is observed for both coherent as well as dissipative coupling, and for a broad range of parameter regimes. In the spirit of mutual synchronization, we investigate the parameter regime where all subsystems are in the broken symmetry phase. We observe that more broadly detuned time crystals require weaker coupling strength to be synchronized. This is in contrast to basic knowledge from classical as well as quantum synchronization theory. We show that this surprising observation is a direct consequence of the seeding effect.