Rydberg Atoms in a Ladder Geometry: Quench Dynamics and Floquet Engineering

Abstract

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 semi-staggered detuning profile. As the staggering strength ($Δ) $ is varied from $0\rightarrow\infty$, the model exhibits a wide class of dynamical phenomena, ranging from quantum many-body scars (QMBS) ($Δ\sim 0,1$) to integrability induced slow dynamics and approximate Krylov fractures ($Δ\ge 2$). 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 (DTC) 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.

Figures (31)

• Figure 1: Schematic representation of the 2-leg Rydberg atom square ladder setup with a semi-staggered detuning profile $\Delta_{j,a}=(-1)^j\Delta$. The dashed gray line shows spatial reflection symmetry axes. The kinetic constraint i.e., the strong Rydberg blockaded regime is illustrated as follows: if an atom is in the $\ket{\bullet} \equiv \ket{\uparrow}$ state (Rydberg excited state, denoted by the red sphere), then all its neighboring atoms must be in the $\ket{\circ} \equiv \ket{\downarrow}$ state (electronic ground-state, denoted by blue spheres) and cannot be flipped to the $\ket{\bullet}$ state under the action of the Hamiltonian \ref{['main:eq:hamiltonian_ladder']}.
• Figure 2: Schematic representation of the phenomenology of quench dynamics of model \ref{['main:eq:hamiltonian_ladder']} when a single parameter $\Delta$ is varied.
• Figure 3: Comparison of the many-body spectrum of $\hat{H}$, $\hat{H}^{[2]}_{\text{eff}}$ and $\hat{H}^{[4]}_{\text{eff}}$ for $\Delta=1,3$ with $N=16$ atoms obtained via ED. (only the middle part of the spectrum is shown).
• Figure 4: Inset: Distribution of consecutive level spacing ratios ($P(r)$) for $\Delta=1,2$ with translation quantum numbers $k_{x,y}=\pi$ (see Appendix-\ref{['app-hsd']}) obtained via ED. Main panel: Disorder averaged mean consecutive level spacing ratio $\langle\!\langle r \rangle\!\rangle$ as a function of staggered detuning strength $\Delta$ for $N=24$ sites (averaged over 100 disorder realizations).
• Figure 5: Top panel: Evolution of quasi-conserved charge $\langle\hat{Q}_1\rangle(t)$ with time under the full Hamiltonian at various values of $\Delta$ starting from the initial state $\ket{\substack{\bullet\circ\circ\bullet\circ\bullet\circ\circ\\\circ\circ\circ\circ\bullet\circ\circ\circ}}$ for $N=16$ sites. Bottom panel: Slow dynamics from other initial states at $\Delta=2$. Time-evolution of the states have been performed via ED method.