Rydberg atom quantum simulator platforms are novel quantum simulators for physical systems ranging from condensed matter to particle physics. In this paper, we study out-of-equilibrium quantum dynamics in a model of Rydberg atoms arranged in ladder geometries, with a semistaggered detuning profile. As the staggering strength ($\mathrm{\Delta })$ is varied from $0\to \infty$, the model exhibits a wide class of dynamical phenomena, ranging from quantum many-body scars ($\mathrm{\Delta }\sim 0,1$) to integrability induced slow dynamics and approximate Krylov fractures ($\mathrm{\Delta }\ge 2$). We study the robustness of these dynamical features against inevitable influences from the environment in the form of pure dephasing and the finite lifetime of the Rydberg excited state. Additionally, by leveraging an underlying spectral reflection symmetry, we design Floquet protocols having dynamical signatures reminiscent of discrete-time-crystalline order and exact Floquet flat bands, and study their stability under protocol imperfections. Finally, we consider long-range van der Waals interactions and investigate the validity of the kinetic constraints in an out-of-equilibrium scenario.

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• Long-range interactions
• Nonequilibrium statistical mechanics
• Open quantum systems & decoherence
• Quantum statistical mechanics
• Time crystals
• Rydberg atoms & molecules
• Trapped atoms
• Exact diagonalization