Prethermalization in the PXP model under continuous quasiperiodic driving

Motivated by recent experiments realizing long-lived nonequilibrium states in aperiodically driven quantum many-body systems, we investigate the dynamics of a quasiperiodically driven Rydberg atom chain in the strong Rydberg blockage regime. In this regime, the system is kinetically constrained and the ``PXP'' model describes its dynamics. Even without driving, the PXP model exhibits many-body scarring and resultant persistent oscillations for dynamics originating from the N\'eel-ordered initial state. We demonstrate that a rich array of dynamical behaviors emerge when the system is subjected to a continuous drive. In the high-frequency regime, the system exhibits revivals and oscillations for the N\'eel ordered initial state both for periodic and quasiperiodic drives. We trace the origin of this nonergodicity to an effective PXP Hamiltonian for both of these driving protocols in this regime. Furthermore, we demonstrate that the behavior of the fidelity and the entanglement entropy is nonmonotonic at low frequencies in the high-amplitude regime. This leads to several re-entrant scarring transitions both for both the N\'eel-ordered and the fully polarized initial state. Our results demonstrate that continuous quasiperiodic drive protocols can provide a promising route to realize prethermal phases of matter in kinetically constrained systems.