Probing emergent prethermal dynamics and resonant melting on a programmable quantum simulator

TL;DR

The work investigates how large, non-integrable quantum systems avoid immediate thermalization after a quench, uncovering Floquet-like prethermal dynamics and resonant melting on a programmable neutral-atom simulator. By combining 1D and 2D Rydberg-spin lattices with diagonal and island observables, the authors identify a robust central prethermal regime and a hierarchy of resonances that melt prethermal states in a controlled, spectrally structured way, including a two-island resonance with a rich effective Hamiltonian. In 2D, a sharp dynamical-edge phenomenon linked to Néel-order defects emerges, suggesting a proximate dynamical phase transition at prethermal times that lacks a direct equilibrium analog. Collectively, the results demonstrate the power of quantum simulation to reveal intricate non-equilibrium quantum many-body phenomena, bridging Floquet prethermalization, resonance-driven dynamics, and emergent dynamical phases beyond equilibrium phase diagrams.

Abstract

The dynamics of isolated quantum systems following a sudden quench plays a central role in many areas of material science, high-energy physics, and quantum chemistry. Featuring complex phenomena with implications for thermalization, non-equilibrium phase transitions, and Floquet phase engineering, such far-from-equilibrium quantum dynamics is challenging to study numerically, in particular, in high-dimensional systems. Here, we use a programmable neutral atom quantum simulator to systematically explore quench dynamics in spin models with up to 180 qubits. By initializing the system in a product state and performing quenches across a broad parameter space, we discover several stable, qualitatively distinct dynamical regimes. We trace their robustness to Floquet-like prethermal steady states that are stabilized over long emergent timescales by strong dynamical constraints. In addition, we observe sharp peaks in the dynamical response that are quantitatively explained by the structured melting of prethermalization through resonances. In two dimensions, we uncover a sharp dynamical response change that converges with increased system size, that is linked to the proliferation of Néel-order defects and indicative of a dynamical phase transition with no equilibrium analogs. Uncovering an intricate interplay between quantum prethermalization and emergent dynamical phases, our results demonstrate the use of quantum simulators for revealing complex non-equilibrium quantum many-body phenomena.

Figures (16)

• Figure 1: The emergence of distinct dynamical regimes in neutral atom quench experiments.a. Rubidium atoms are arranged in square grids (2D) or square chains with flattened corners (1D), and they are driven by constant quenches in the detuning field $\Delta$ and the Rabi frequency $\Omega$. Dynamics couples ground states (purple spheres, white tiles) and excited states (red spheres, black tiles) with a range of interaction strengths as measured by the blockade radius $R_\mathrm{b}$. b. The atoms are initialized in the all-zero state, with post-quench excitations proliferating until the system reaches a non‑equilibrium steady state. Steady-state sampling reveals a sequence of dynamical regimes, each defined by the stable long-time averages of key local observables. As the detuning quench strength increases, spatial excitation patterns evolve: from i. isolated excitations, to ii. mixed-excitation domains, to iii. large, defect-rich checkerboards, to abrupt regime changes, and iv. at still higher detunings, to the emergence of isolated multi-excitation island patterns. Comparable behavior is observed in the one-dimensional chain.
• Figure 2: Dynamical regimes of the 1D chain. Distinct dynamical regimes are extracted from long-time quench dynamics in experiments (up to 4$\, \mathrm{\mu s}$ time evolution) with $52$ atoms and numerics with $16$ atoms (up to 10$\, \mathrm{\mu s}$ time evolution in a and up to 100$\, \mathrm{\mu s}$ in d). a. Dynamical phase diagrams (experiment left, numerics right) displaying the time-averaged expectation value of the two-site observable $\hat{O}_{ZZ}$, revealing a central region and side resonances. The atom schematics in the upper left corners show the geometries. The red dashed horizontal line represents the cut $R_\mathrm{b} / a = 1.4$, while the gray dashed line satisfies $V_1 = 2\Delta$. b. The time evolution of $\langle\hat{O}_{ZZ}\rangle$ for characteristic points on the cut. c. Schematic overview of the phenomenology of the different dynamical regimes. The integer structure of the energy spectrum at small $\Delta$ and $\Omega$ results in an effective Floquet-like drive that induces prethermalization in the blockade subspace. In the side peaks, the spectral gaps become commensurate with the drive frequency, providing heating pathways for prethermalization melting via resonances on specific excitation patterns. d. The time-averaged expectation values of the two-site observable $\hat{O}_{ZZ}$ on the $R_\mathrm{b} / a = 1.4$ cut (experiment and numerics), and the thermal expectation values of the observable for the effective temperature of the quench using the nearest-neighbor blockade subspace (thermal blockade) and the full Hilbert space (thermal full).
• Figure 3: Experimental characterization of the central region and resonances for the 1D chain.a. The Hamming weight ($\hat{Q}_n$) distribution of experimentally and numerically sampled post-quench states along the representative cut $R_\mathrm{b} / a = 1.4$ at a fixed system size $N$. At $\Delta/\Omega = 0$ (inset), the excitation distribution exhibits a mean of $N/4$ and a variance of $N/8$ across experimentally probed system sizes, consistent with equal excitation probability across the blockade subspace. b. The time-averaged expectation values of the $k$-island observables for $k = 1,2,3$ (illustrated in the legend) resolve the fan of side peaks in the experiment. The island operator peaks coincide with resonances between the energy of island excitations and the initial state. The sub-peaks indicate sub-dominant contributions of the island mixtures to a given resonance.
• Figure 4: Dynamical regimes of the 2D lattice.a. Decomposed experimental dynamical phase diagrams for $180$ atoms displaying the time-averaged expectation values of several $k$-island observables. $\hat{O}_H^{(k)}$ and $\hat{O}_L^{(k)}$ measure islands with and without diagonal blockade restrictions, respectively, according to shapes and sizes shown in the schematics. The grey dashed horizontal lines show the representative cut $R_\mathrm{b} / a = 1.4$, the focus of panels b-d. b. The time-averaged expectation values of the $1$-island observables on the cut for different lattice sizes $N$. The black dashed vertical lines show the locations $\Delta / \Omega = c (R_\mathrm{b} / a)^6$ for $c = 1/16 , 1/4$, which correspond to the smallest and largest resonant Néel order patches in the classical limit, shown by the atom schematics. c. The time-averaged expectation values of the island operator sum on the cut $R_\mathrm{b} / a = 1.4$ for $16$ atoms, and the thermal expectation values of the observable for the effective temperature of the quench using the nearest-neighbor blockade subspace (thermal $xy$ blockade) and the full Hilbert space (thermal full). d. The time-averaged response of the classical spin dynamics model, obtained from the $S \rightarrow \infty$ limit of the quantum spins, and the quantum counterpart for $180$ atoms, on the cut $R_\mathrm{b} / a = 1.4$. The classical response exhibits a dynamical phase transition (black dashed vertical line) given by the approximate solution to the Stoner-Wohlfarth astroid (Supplementary Information). A schematic shows representative dynamics on either side of the classical transition, and similarly for the quantum analog.
• Figure 5: Experimental geometries and waveforms. The lattices are shown for $R_\mathrm{b} / a = 1.4$. 1D lattice with a. 52 atoms; and b. 16 atoms, where the field of view can accommodate 2 parallel copies with separation $b = 5a$. 2D square lattice with c. 180 atoms; and d. 16 atoms, where the field of view can accommodate 6 parallel copies with separation $b = 5a$. e. Pulse sequences. (Top) The Rabi frequency $\Omega$ is set to a constant value $\Omega / 2\pi = 2.5$ MHz. (Bottom) The detuning $\Delta$ is set in the range $\Delta / \Omega \in [-4.0, 6.0]$, and shown here for $\Delta / \Omega = 0.4$.