Emergent disorder and sub-ballistic dynamics in quantum simulations of the Ising model using Rydberg atom arrays

TL;DR

Emergent disorder and sub-ballistic dynamics arise when simulating the transverse-field Ising model with Rydberg atom arrays. The authors combine remote Aquila experiments with tensor-network simulations and a minimal random-spin model to show that atomic motion at finite temperature generates effective disorder, slowing information spread and producing logarithmic entanglement growth $S(t) \sim \log t$. By varying lattice spacing and drive strength, they map out localized-like and delocalized-like regimes and reveal how motion, rather than blockade constraints, dominates TFIM dynamics at the blockade radius. The results underscore the need to account for motion and decoherence in Rydberg-based quantum simulations and offer simple benchmarking protocols to diagnose motion-induced disorder in future experiments.

Abstract

Rydberg atom arrays with Van der Waals interactions provide a controllable path to simulate the locally connected transverse-field Ising model (TFIM), a prototypical model in statistical mechanics. Remotely operating the publicly accessible Aquila Rydberg atom array, we experimentally investigate the physics of TFIM far from equilibrium and uncover significant deviations from the theoretical predictions. Rather than the expected ballistic spread of correlations, the Rydberg simulator exhibits a subballistic spread, along with a logarithmic scaling of entanglement entropy in time - all while the system mostly retains its initial magnetization. By modeling the atom motion, we trace these effects to an emergent disorder in Rydberg atom arrays, which we characterize with a minimal random spin model. We further experimentally explore the different dynamical regimes hosted in the system by varying the lattice spacing and the Rabi frequency. Our findings highlight the crucial role of atom motion in the many-body dynamics of Rydberg atom arrays at the TFIM limit, and propose simple benchmark measurements to test for its presence in future experiments.

Figures (13)

• Figure 1: A measurement sequence on Aquila atom array trapped in tweezers with all atoms in the ground state at $t=0$ evolving to the final state measured at $t=3\mu$s. The machine images, provided by QuEra Computing, shows our lattice geometry and the pulse sequence of the experiment where the Rabi frequency $\Omega$ and the detuning $\Delta$ are suddenly quenched, i.e., ramped in $50$ns. Due to thermal fluctuations, atoms move which gives rise to a positional uncertainty $\delta r$.
• Figure 2: (a) Measured and (b) simulated lightcone of quasi-particles generated following a quench to Rabi frequency $\Omega = 2.2 \text{ rad}/\mu$s at the TFIM limit and plotted with perceptually uniform colormaps. The quasi-particles slow down due to atom motion following a subballistic lightcone, solid-white, instead of ballistic, solid-red. (c) Measured (markers) and simulated (shades) magnetization $\mathcal{M}(t)$ and domain-wall density $\mathcal{G}(t)$ compared to the ideal simulation (dotted). (d) Simulated bi-partite entanglement entropy $S(t)$ (shade), and measured (marker) and simulated (shade) quantum Fisher information density $\mathcal{F}_Q(t)/L$, all exhibiting a logarithmic scaling in time when atom motion is modeled. The solid-black line is used to guide the line to show the logarithmic scaling. The ideal $S(t)$ and $\mathcal{F}_Q(t)/L$ are linear and power-law in time, respectively. All error bars are standard error of the mean (s.e.m).
• Figure 3: Naturally disordered quantum many-body system following a quench to $\Omega=11.7$ rad$/\mu$s at the TFIM limit numerically (shades) and experimentally (markers) probed with (a) Quantum Fisher information (QFI) density and (b) magnetization for different lattice constants. Panels (a): (a$_1$), (a$_2$), (a$_3$) and (a$_4$) respectively plot the QFI density for $a=7\mu$m, $a=8\mu$m, $a=7.5\mu$m and $a=10.5\mu$m. Panels (b): (b$_1$) and (b$_2$) respectively plot the magnetization for $a=7\mu$m and $a=8\mu$m. For (a) and (b), the legends include the results of the experiment, ideal setup with no atom motion (dotted), the minimal model (MM) in Eq. \ref{['eq:emergentSpin']} modeling the atom motion in the presence and absence of decoherence. Fig. (a$_1$) is plotted in semi-log scale to show the logarithmic increase of QFI density in time. (c) The positional uncertainty $\delta r$ for different lattice constants in the unitary and decohering MM and (d) the resulting disorder strength $\mathcal{W}$. All error bars are s.e.m. Error bars for the MM are due to 10 different statistically similar systems with different configurations of $J_r$ and $h_r$.
• Figure 4: Time-averaged (a) magnetization and (b) domain-wall density to experimentally probe a trace of $Z_2$ symmetry breaking of spontaneous symmetry breaking transition at the clean TFIM. Experiments are performed with quenches to different Rabi frequencies $\Omega$ and hence transverse field $h_x$ at the TFIM limit at fixed lattice constant $a=9\mu$m. Orange-stars are the simulated results with all uncertainties included. Inset in (a) zooms on the crossover region. (b) also shows the ideal TFIM results in the infinite time limit with red-dashed line. All error bars are s.e.m.
• Figure 5: Comparison of the QFI results from tensor network simulations of Rydberg atom array with atom motion treated classically and the time-evolution of minimal model Eq. \ref{['eq:emergentSpin']} where $\delta_r=0.1\mu$m for lattice spacing $a=7\mu$m (left panel) and $a=8\mu$m (right panel) at $\Omega=11.7$ rad/$\mu$s.