Signatures of discrete time crystalline order in dissipative spin ensembles

James O’Sullivan,Arijeet Pal,M L W Thewalt,Christoph W Zollitsch,Oliver Lunt,John J L Morton

doi:10.1088/1367-2630/ab9fbe

Abstract

Discrete time-translational symmetry in a periodically driven many-body system can be spontaneously broken to form a discrete time crystal, an exotic new phase of matter. We present observations characteristic of discrete time crystalline order in a driven system of paramagnetic P-donor impurities in isotopically enriched 28Si cooled below 10 K. The observations exhibit a stable subharmonic peak at half the drive frequency which remains pinned even in the presence of pulse error, a signature of discrete time crystalline order. This signal has a finite lifetime of ∼100 Floquet periods, but this effect is long-lived relative to coherent spin–spin interaction timescales, lasting ∼104 times longer. We present simulations of the system based on the paradigmatic central spin model and show good agreement with experiment. We investigate the role of dissipation and interactions within this model, and show that both are capable of giving rise to discrete time crystal-like behaviour.

Highlights

A central paradigm in condensed matter physics has been to classify phases of matter by their symmetries
In this article we report the observation of signatures of a discrete time crystal (DTC) in silicon doped with phosphorus
In the absence of interactions between electron spins, when we increase on the π-pulse in each Floquet cycle we expect the cumulative error caused by successive over- or under-rotation of the spin ensemble to cause modulation of the oscillations

Summary

Introduction

A central paradigm in condensed matter physics has been to classify phases of matter by their symmetries. A common symmetry-breaking phase is a crystal in real space, where the symmetry under continuous spatial translation is broken to a lower discrete one. A natural question is to ask whether it is possible to analogously break time-translation symmetry [1]. Breaking of continuous time-translation symmetry has been shown to be impossible in thermal equilibrium [2, 3], but periodically-driven (‘Floquet’) systems provide the means to break discrete time-translation symmetry, thereby forming a discrete time crystal [4,5,6,7,8,9,10]. Observations consistent with discrete time-crystalline behaviour were reported soon after in experiments [11,12,13,14]

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Conclusion