Time crystallinity in open quantum systems

TL;DR

This paper investigates the existence and stability of time crystals in open quantum systems, highlighting how dissipation and noise influence their non-equilibrium time-translational symmetry breaking.

Contribution

It introduces a novel method to identify open system time crystals using the Floquet propagator and demonstrates their behavior in short-range interacting open systems.

Findings

Time crystals can exist in open quantum systems.

The nature of decay processes affects time-crystalline order.

A Floquet propagator-based approach effectively identifies open system time crystals.

Abstract

Time crystals are genuinely non-equilibrium quantum phases of matter that break time-translational symmetry. While in non-equilibrium closed systems time crystals have been experimentally realized, it remains an open question whether or not such a phase survives when systems are coupled to an environment. Although dissipation caused by the coupling to a bath may stabilize time crystals in some regimes, the introduction of incoherent noise may also destroy the time crystalline order. Therefore, the mechanisms that stabilize a time crystal in open and closed systems are not necessarily the same. Here, we propose a way to identify an open system time crystal based on a single object: the Floquet propagator. Armed with such a description we show time-crystalline behavior in an explicitly short-range interacting open system and demonstrate the crucial role of the nature of the decay processes.