  We study the population trapping extensively in a periodically driven Rydberg
pair. The periodic modulation of the atom-light detuning effectively suppresses
the Rabi couplings and, together with Rydberg-Rydberg interactions, leads to
the state-dependent population trapping. We identify a simple yet a general
scheme to determine population trapping regions using driving induced
resonances, the Floquet spectrum, and the inverse participation ratio. Contrary
to the single atom case, we show that the population trapping in the two-atom
setup may not necessarily be associated with level crossings in the Floquet
spectrum. Further, we discuss under what criteria population trapping can be
related to dynamical stabilization, taking specific and experimentally relevant
initial states, which include both product and the maximally entangled Bell
states. The behavior of the entangled states is further characterized by the
bipartite entanglement entropy.
