  The conventional framework for defining and understanding phases of matter
requires thermodynamic equilibrium. Extensions to non-equilibrium systems have
led to surprising insights into the nature of many-body thermalization and the
discovery of novel phases of matter, often catalyzed by driving the system
periodically. The inherent heating from such Floquet drives can be tempered by
including strong disorder in the system, but this can also mask the generality
of non-equilibrium phases. In this work, we utilize a trapped-ion quantum
simulator to observe signatures of a non-equilibrium driven phase without
disorder: the prethermal discrete time crystal (PDTC). Here, many-body heating
is suppressed not by disorder-induced many-body localization, but instead via
high-frequency driving, leading to an expansive time window where
non-equilibrium phases can emerge. We observe a number of key features that
distinguish the PDTC from its many-body-localized disordered counterpart, such
as the drive-frequency control of its lifetime and the dependence of
time-crystalline order on the energy density of the initial state. Floquet
prethermalization is thus presented as a general strategy for creating,
stabilizing and studying intrinsically out-of-equilibrium phases of matter.
