  We study the prethermal Floquet phases of a two-dimensional (2D) Rydberg atom
array on a rectangular lattice in the presence of a periodic drive with large
drive amplitude. We derive an analytic, albeit perturbative, Floquet
Hamiltonian using Floquet perturbation theory (FPT) which charts out these
phases and shows that the transition between them can be accessed by tuning the
drive frequency. Using both numerical exact diagonalization on finite-size
arrays and analytical first-order Floquet Hamiltonian derived using FPT, we
show that these prethermal Floquet phases and the transitions between them can
be detected by studying the dynamics of equal-time density-density correlation
functions of the Rydberg atoms. Our analysis thus provides a simple way of
detecting these phases and associated transitions in this system; such a
detection can be achieved in standard experiments which we discuss.
