# Clean Floquet Time Crystals: Models and Realizations in Cold Atoms

## TL;DR

This paper demonstrates that time crystals can exist in disorder-free systems using Floquet driving in cold atom models, supported by theoretical analysis and proposed experimental realizations.

## Contribution

It introduces clean, disorder-free models for Floquet time crystals and suggests feasible cold atom experiments to realize them.

## Key findings

- Time crystals can exist without disorder in Floquet systems.
- Strong interactions and emergent integrals of motion stabilize the phase.
- Proposed cold atom schemes for experimental realization.

## Abstract

Time crystals, a phase showing spontaneous breaking of time-translation symmetry, has been an intriguing subject for systems far away from equilibrium. Recent experiments found such a phase both in the presence and absence of localization, while in theories localization by disorder is usually assumed a priori. In this work, we point out that time crystals can generally exist in systems without disorder. A series of clean quasi-one-dimensional models under Floquet driving are proposed to demonstrate this unexpected result in principle. Robust time crystalline orders are found in the strongly interacting regime along with the emergent integrals of motion in the dynamical system, which can be characterized by level statistics and the out-of-time-ordered correlators. We propose two cold atom experimental schemes to realize the clean Floquet time crystals, one by making use of dipolar gases and another by synthetic dimensions.