Dynamics of string breaking and revival in a Rydberg atomic chain

TL;DR

This work investigates confinement-like string-breaking dynamics in a one-dimensional Rydberg atomic chain by mapping domain-wall pairs to mesons and contiguous excitations to strings. By tuning the string tension via detuning $\\Delta$ and the driving strength $\\Omega$, the authors identify two dynamical regimes: string breaking into meson configurations and localized revival where the initial string partially reappears. They quantify these dynamics using the string survival probability $P(t)$, domain-wall density, and half-chain entanglement entropy $S(t)$, and they reveal how quantum fluctuations reshape the configuration weights, increasing double-meson content without destroying single-meson dominance. A two-parameter scan in $(\\Delta,\\Omega)$ uncovers a robust $V$-shaped structure in long-time averages, linking confinement-like physics to observable, tunable quantum-simulation platforms and offering guidance for experimental exploration of string dynamics and entanglement generation.

Abstract

String breaking is one of the most representative nonperturbative dynamics processes in confinement theory, typically associated with the creation of particle-antiparticle pairs. In this paper, we take a one-dimensional Rydberg atomic chain to theoretically study the dynamical of finite-length string state. Under different string tension conditions, we find that the string dynamics exhibits two clearly distinguishable evolution characteristics: one is that the string breaks and the system enters a superposition state space containing multiple meson state configurations; the other is localized string dynamics, in which the string undergoes local breaking but can then recombine and return to a state close to the initial structure, with the breaking and recombination processes recurring over a long time scale. Through the analysis of the evolution of different meson state configurations, we visually depict the redistribution of configuration weights during the string breaking process, and reveal the observable recovery characteristics of the string after breaking. Further analysis shows that the enhancement of quantum fluctuations can increase the weight of the double-meson state configurations in the system wave function without changing the dominant dynamical behavior. The above results present a rich picture of string breaking dynamics in a one-dimensional Rydberg atomic chain and provide insights for studying confinement physics and related gauge field theory phenomena on quantum simulation platforms.

Figures (5)

• Figure 1: The string-meson physical picture and dynamics in a Rydberg atomic chain. (a) Schematic diagram of a one-dimensional Rydberg atomic chain and the corresponding string-meson mapping. Each atom is modeled as a two-level system consisting of the ground state $\ket{g}$ and the Rydberg excited state $\ket{r}$, coherently coupled by a laser field with Rabi frequency $\Omega$ and detuning $\Delta$. Configurations $\ket{gr}$ and $\ket{rg}$ correspond to domain-wall excitations and are mapped to particle–antiparticle pairs. A contiguous region of Rydberg excitations bounded by two domain walls is mapped to a string. During the dynamical evolution, the initial single-meson state undergoes string breaking, generating two mesons, which subsequently recombine, in correspondence with the numerical results shown in panels (b) and (c). (b) Time evolution of the Rydberg excitation probability $n_{i}(t)$ and the domain wall density $D_{i}(t)$ as heat maps versus the dimensionless time $Vt$. The horizontal axes correspond to the atomic site index and the bond index, respectively, while the vertical axis represents the dimensionless time $Vt$, and the color scale indicates the magnitude of the domain wall density. (c) Time evolution of the string survival probability $P(t)$ and the half-chain entanglement entropy $S(t)$ as functions of $Vt$.
• Figure 2: Meson configurations and string length dynamics during the string breaking process. (a) Examples of the main single-meson (top) and double-meson (bottom) configurations that the system can evolve into from the initial single-meson state with string length $l = 4$ at $Vt = 2\pi\times6$. (b) The occurrence probabilities of various configurations in (a). (c) Time evolution of string length distribution in the single-meson (top) and double-meson (bottom) subspaces with $Vt$. The horizontal axis represents time $Vt$, the vertical axis represents string length $l$, and the color bar indicates the probability of occurrence of that string length.
• Figure 3: The dynamical evolution of finite-length string states (initial string length $l=4$) under different detuning parameters. In Figs (a)-(c), the dynamical results of the system are presented for fixed interaction strength $V$ and detuning parameters $\Delta=2\pi\times11~\mathrm{MHz}$ (a), $\Delta=2\pi\times11.5~\mathrm{MHz}$ (b),and $\Delta=2\pi\times12~\mathrm{MHz}$ (c), respectively. In each column, from top to bottom, the evolution heat map of domain wall density on each bond of the atomic chain with time $Vt$, the string survival probability $P(t)$, and the half-chain entanglement entropy $S(t)$ with time $Vt$ are displayed. Under different detuning parameters, the three dynamical observables exhibit significantly different time evolution characteristics.
• Figure 4: The influence of driving intensity on string evolution and meson configurations. (a) Evolution heat map of domain wall density over time under fixed interaction strength $V$ and detuning parameter $\Delta$. The upper and lower plots correspond to $\Omega/(2\pi) = 0.8~\mathrm{MHz}$ and $\Omega/(2\pi) = 1.2~\mathrm{MHz}$, respectively, for comparing the influence of domain wall fluctuations and spatial distribution under different driving intensities. (b) At a fixed time slice $Vt = 2\pi\times6$, the total probability weights of the system wave function projected onto different meson subspaces. Shown are the total probability $P_2$ of single-meson configurations and the total probability $P_4$ of double-meson configurations as functions of $\Omega$. (c) At the same time slice $Vt = 2\pi\times6$, the string length distribution is statistically analyzed in the single-meson subspaces and double-meson subspaces, showing the influence of the driving intensity on the internal length structure of the configuration.
• Figure 5: The long-term average distribution of string survival probability and half-chain entanglement entropy within the $(\Delta, \Omega)$ parameter space. (a) The two-dimensional heatmap of the long-term average value $\bar{P}$ of string survival probability in the $(\Delta, \Omega)$ parameter space. (b) The two-dimensional heatmap of the long-term average value $\bar{S}$ of half-chain entanglement entropy in the same parameter space. With $\Omega/(2\pi)\in[0.8, 1.2]~\mathrm{MHz}$, and uniformly selecting $50$ parameter points within the interval of $\Delta/(2\pi)\in[9, 15]~\mathrm{MHz}$ for two-dimensional scanning. The color bar respectively represents the numerical magnitudes of $\bar{P}$ and $\bar{S}$.