  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.
