Observation of an anomaly in the statistics of Kibble-Zurek defects

TL;DR

The paper probes whether Kibble-Zurek (KZ) defect statistics obey universal scaling in a non-integrable, one-dimensional Rydberg-chain system, revealing a ramp-rate–dependent anomaly in defect counting statistics. Using up to 58 atoms, the authors measure full defect-count distributions across a $\\Z_2$ transition and find that, at slow ramps, the variance exceeds the mean, signaling correlated defects beyond independent-domain mergers; this is corroborated by exact-diagonalization simulations that show long-range defect correlations arising from post-critical non-critical coarsening. A prepare-and-hold protocol suppresses coarsening and restores conventional (Poisson-like) statistics, highlighting a controlled freeze-out of correlations and delineating the limits of KZ universality in non-integrable 1D systems. The work demonstrates that quantum simulators can uncover unexpected correlated quantum phenomena and connect defect statistics to non-critical dynamics deep in the ordered phase.

Abstract

The Kibble-Zurek mechanism quantifies defect formation during adiabatic passage across a continuous phase transition, providing key insights into universality in quantum many-body systems. We explore counting statistics of defects in adiabatic passage experiments on long 1D Rydberg atom chains. The experiments reveal an anomaly in the defect number distribution at long ramp times, challenging the hypothesis of defect formation through independent domain mergers. Numerical simulations confirm the anomaly and suggest its link to non-critical coarsening dynamics, which we suppress in prepare-and-hold experiments. Our results highlight the ability of quantum simulators to uncover unexpected correlated quantum phenomena.

Figures (9)

• Figure 1: Kibble-Zurek defect formation and statistics anomaly. (a) Schematic of a Rydberg atom array with Ising spins (orange/brown dots). As the system is driven from a paramagnetic phase 'a' through the vicinity of a critical point 'b' into the antiferromagnetic phase, pre-domains of antiferromagnetic order develop on a correlation length ($\xi$) scale. The mergers between the domains result in the formation (black) or absence (white) of the domain wall defect at random. This results in the Poisson-binomial defect counting statistics at time point 'b', with variance proportional to, and smaller than, the mean, and uncorrelated defects (top right). (b) For slow driving rates $\Gamma$, we observe that defects become correlated through coarsening dynamics deep within the antiferromagnetic phase lobe, 'c', resulting in a defect counting statistics anomaly (bottom right).
• Figure 2: Experimental setup and correlation length measurement. (a) The 58 atom geometry chosen to fit in the Aquila simulator Wurtz2023 field of view. Red circles indicate the atom positions separated by $a=6.2~ \mu \mathrm{m}$, and semi-transparent blue circles show blockade radii $R_b / a = 1.35$. (b) The Rabi frequency $\Omega(t)$ and detuning $\Delta(t)$ drives used to adiabatically prepare ground states of the antiferromagnetic phase. The blue shaded region shows the variable detuning ramp time $t_\Delta \in [0,3]\mu$s. (c) The two-point Rydberg density correlations $|\langle \tilde{n}_i \tilde{n}_{i+l} \rangle_c|$ ($\tilde{n}=n-1/2$) as a function of distance $l$ for different ramp times. The solid lines show exponential fits over $l \in [1,6]$ used to extract correlation lengths. (d) The defect correlation length vs the quench rate $\Gamma$. For intermediate-ramp-rate quenches, the behavior approaches the expected $\mu=0.5$ Kibble-Zurek scaling (red line).
• Figure 3: Anomaly in the defect counting statistics. Domain wall mean (blue) and variance (red) vs the quench rate $\Gamma$ from (a) experiments and (b) numerical simulations rescaled by the size ratio $58/24$. The vertical error bars denote experimental statistical errors, and the bands denote the systematic errors due to zero--readout noise mitigation. In both experiments and numerics, we observe a salient regime at lower quench rates where the defect variance exceeds the mean. The discrepancy is associated with the development of non-trivial defect correlations. In numerics, we compare the connected correlators of the density-density and defect-defect observables: (c) for slow ramps, domain walls are anticorrelated, coinciding with a statistics anomaly; (d) at faster ramps, domain wall correlations simply follow the correlation length determined by density correlations.
• Figure 4: Hold protocol and dynamics. (a) By appending the time constant protocol for a hold time $t_h$ after the ramp, we probe the non-critical dynamics at fixed energy. Both in (b) experiment and (c) simulations, correlation lengths and domain wall numbers are stable in time, indicating a freeze out of the coarsening dynamics. Simulations further recover oscillatory behavior absent in experiments due to dephasing.
• Figure 5: Zero-noise extrapolation (ZNE) for readout error mitigation. The two-step ZNE procedure is shown for the mean wall number (top row) and wall number variance (bottom row) at three different ramp times $t_\Delta$ (columns a-c). The process starts with raw experimental data (red circle at $\epsilon_{10}^{\text{true}}$) and data points where noise has been artificially amplified (orange triangles and purple squares). First, a linear extrapolation in the $\epsilon_{01}$ error is performed for fixed values of $\epsilon_{10}$ to obtain the partially-mitigated intermediate data (green diamonds). Second, these intermediate points are extrapolated to the zero-noise limit ($\epsilon_{10} \to 0$). A linear model (blue line) is sufficient for the mean wall number, while a quadratic model is required for the variance. The final, fully error-mitigated value is the extrapolated point at $\epsilon_{10}=0$ (blue open circle). The dashed green lines represent the one-standard-deviation confidence interval of the fit.