Shattered Time: Can a Dissipative Time Crystal Survive Many-Body Correlations?

TL;DR

This paper explores the formation and stability of a dissipative time crystal in a driven many-body spin system, highlighting the role of many-body correlations and collective interactions in spontaneous time symmetry breaking.

Contribution

It demonstrates that a dissipative time crystal can spontaneously break time symmetry through elastic interactions without external drive, and analyzes the impact of many-body correlations on its stability.

Findings

Time crystal stability linked to slow mutual information growth

Time crystal remains robust against single-particle dephasing

Connection established between many-body correlations and emergent semi-classical states

Abstract

We investigate the emergence of a time crystal in a driven-dissipative many-body spin array. In this system the interplay between incoherent spin pumping and collective emission stabilizes a synchronized non-equilibrium steady state which in the thermodynamic limit features a self-generated time-periodic pattern imposed by collective elastic interactions. In contrast to prior realizations where the time symmetry is already broken by an external drive, here it is only spontaneously broken by the elastic exchange interactions and manifest in the two-time correlation spectrum. Employing a combination of exact numerical calculations and a second-order cumulant expansion, we investigate the impact of many-body correlations on the time crystal formation and establish a connection between the regime where it is stable and a slow growth rate of the mutual information, signalling that the time crystal studied here is an emergent semi-classical out-of-equilibrium state of matter. We also confirm the rigidity of the time crystal to single-particle dephasing. Finally, we discuss an experimental implementation using long-lived dipoles in an optical cavity.