Dynamics of the vacuum state in a periodically driven Rydberg chain

We study the dynamics of a periodically driven Rydberg chain starting from the state with zero Rydberg excitations (vacuum state denoted by vertical bar 0 >) using a square pulse protocol in the high drive amplitude limit. We show, using exact diagonalization for finite system sizes (L <= 26), that the Floquet Hamiltonian of the system, within a range of drive frequencies that we chart out, hosts a set of quantum scars that have large overlap with the vertical bar 0 > state. These scars are distinct from their counterparts having high overlap with the maximal Rydberg excitation state (vertical bar Z(2)>); they coexist with the latter class of scars and lead to persistent coherent oscillations of the density-density correlator starting from the vertical bar 0 > state. We also identify special drive frequencies at which the system undergoes perfect dynamic freezing, and we provide an analytic explanation for this phenomenon. Finally, we demonstrate that for a wide range of drive frequencies, the system reaches a steady state with subthermal values of the density-density correlator. The presence of such subthermal steady states, which are absent for dynamics starting from the vertical bar Z2 > state, imply a weak violation of the eigenstate thermalization hypothesis in finite-sized Rydberg chains distinct from that due to the scar-induced persistent oscillations reported earlier. We conjecture that in the thermodynamic limit, such states may exist as prethermal steady states that show anomalously slow relaxation. We supplement our numerical results by deriving an analytic expression for the Floquet Hamiltonian using a Floquet perturbation theory in the high amplitude limit, which provides an analytic, albeit qualitative, understanding of these phenomena at arbitrary drive frequencies. We discuss experiments that can test our theory.