  Periodic driving has been established as a powerful technique for engineering
novel phases of matter and intrinsically out-of-equilibrium phenomena such as
time crystals. Recent work by Bluvstein et al. [Science 371, 1355 (2021)] has
demonstrated that periodic driving can also lead to a significant enhancement
of quantum many-body scarring, whereby certain non-integrable systems can
display persistent quantum revivals from special initial states. Nevertheless,
the mechanisms behind driving-induced scar enhancement remain poorly
understood. Here we report a detailed study of the effect of periodic driving
on the PXP model describing Rydberg atoms in the presence of a strong Rydberg
blockade - the canonical static model of quantum many-body scarring. We show
that periodic modulation of the chemical potential gives rise to a rich phase
diagram, with at least two distinct types of scarring regimes that we
distinguish by examining their Floquet spectra. We formulate a toy model, based
on a sequence of square pulses, that accurately captures the details of the
scarred dynamics and allows for analytical treatment in the large-amplitude and
high-frequency driving regimes. Finally, we point out that driving with a
spatially inhomogeneous chemical potential allows to stabilize quantum revivals
from arbitrary initial states in the PXP model, via a mechanism similar to
prethermalization.
