Dynamics of the vacuum state in a periodically driven Rydberg chain

Abstract

We study the dynamics of the periodically driven Rydberg chain starting from the state with zero Rydberg excitations (vacuum state denoted by $|0⟩$) using a square pulse protocol in the high drive amplitude limit. We show, using exact diagonalization for finite system sizes ($L\le 26$), that the Floquet Hamiltonian of the system, within a range of drive frequencies which we chart out, hosts a set of quantum scars which have large overlap with the $|0⟩$ state. These scars are distinct from their counterparts having high overlap with the maximal Rydberg excitation state ($|{\mathbb{Z}}_2⟩$); they coexist with the latter class of scars and lead to persistent coherent oscillations of the density-density correlator starting from the $|0⟩$ state. We also identify special drive frequencies at which the system undergoes perfect dynamic freezing and 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 sub-thermal values of the density-density correlator. The presence of such sub-thermal steady states, which are absent for dynamics starting from the $|{\mathbb{Z}}_2⟩$ 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 pre-thermal 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 which can test our theory.

18 pages and 17 figures including appendices

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