Dynamics of the vacuum state in a periodically driven Rydberg chain

• URL: http://arxiv.org/abs/2005.07715v1
• Date: Fri, 15 May 2020 18:00:03 GMT
• Title: Dynamics of the vacuum state in a periodically driven Rydberg chain
• Authors: Bhaskar Mukherjee, Arnab Sen, Diptiman Sen, K. Sengupta
• Abstract summary: We study the dynamics of the periodically driven Rydberg chain starting from the state with zero Rydberg excitations. We show that the Floquet Hamiltonian of the system, within a range of drive frequencies, hosts a set of quantum scars.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the dynamics of the periodically driven Rydberg chain starting from the state with zero Rydberg excitations (vacuum state denoted by $|0\rangle$) 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 $|0\rangle$ state. These scars are distinct from their counterparts having high overlap with the maximal Rydberg excitation state ($|\mathbb{Z}_2\rangle$); they coexist with the latter class of scars and lead to persistent coherent oscillations of the density-density correlator starting from the $|0\rangle$ 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 $|\mathbb{Z}_2\rangle$ 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.

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