The role of fluctuations in quantum and classical time crystals

TL;DR

This paper investigates the stability of discrete time crystals in a Bose-Hubbard model, revealing no fundamental difference between quantum and classical DTCs when considering fluctuations, and proposes an experimental setup to observe these effects.

Contribution

It demonstrates that fluctuations do not distinguish quantum from classical DTCs in a Bose-Hubbard model, bridging understanding between classical and quantum time crystals.

Findings

No distinction between quantum and classical DTCs regarding fluctuations.

Fluctuations influence the stability of time crystals.

Proposes an experiment with coupled parametric resonators to observe fluctuation effects.

Abstract

Discrete time crystals (DTCs) are a many-body state of matter whose dynamics are slower than the forces acting on it. The same is true for classical systems with period-doubling bifurcations. Hence, the question naturally arises what differentiates classical from quantum DTCs. Here, we analyze a variant of the Bose-Hubbard model, which describes a plethora of physical phenomena and has both a classical and a quantum time-crystalline limit. We study the role of fluctuations on the stability of the system and find no distinction between quantum and classical DTCs. This allows us to probe the fluctuations in an experiment using two strongly coupled parametric resonators subject to classical noise.