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arXiv:2511.15047 · Nature Communications

Time series learning in a many-body Rydberg system with emergent collective nonlinearity

Zongkai Liu, Qiming Ren, Chris Nill, Albert Cabot, Wei Xia, Yanjie Tong, Huizhen Wang, Wenguang Yang, Junyao Xie, Mingyong Jing, Hao Zhang, Liantuan Xiao, Suotang Jia, Igor Lesanovsky, Linjie Zhang

quant-phphysics.atom-phSubmitted Nov 19, 2025• Announced Nov 20, 2025• 0 citations
v1 · Nov 19, 2025v2 · Jun 2, 2026v3 · Jun 3, 2026
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Abstract

Interacting Rydberg atoms constitute a versatile platform for the realization of non-equilibrium states of matter. Close to phase transitions, they respond collectively to external perturbations, which can be harnessed for technological applications in the domain of quantum metrology and sensing. Owing to the controllable complexity and straightforward interpretability of Rydberg atoms, we can observe and tune the emergent collective nonlinearity. Here, we investigate the application of an interacting Rydberg vapour for the purpose of time series prediction. The vapour is driven by a laser field whose Rabi frequency is modulated in order to input the time series. We find that close to a non-equilibrium phase transition, where collective effects are amplified, the capability of the system to learn the input becomes enhanced. This is reflected in an increase of the accuracy with which future values of the time series can be predicted. Using the Lorenz time series and temperature data as examples, our work demonstrates how emergent phenomena enhance the capability of noisy many-body quantum systems for data processing and forecasting.

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Interacting Rydberg atoms constitute a versatile platform for the realization of non-equilibrium states of matter. Close to phase transitions, they respond collectively to external perturbations, which can be harnessed for technological applications in the domain of quantum metrology and sensing. Owing to the controllable complexity and straightforward interpretability of Rydberg atoms, we can observe and tune the emergent collective nonlinearity. Here, we investigate the application of an interacting Rydberg vapour for the purpose of time series prediction. The vapour is driven by a laser field whose Rabi frequency is modulated in order to input the time series. We find that close to a non-equilibrium phase transition, where collective effects are amplified, the capability of the system to learn the input becomes enhanced. This is reflected in an increase of the accuracy with which future values of the time series can be predicted. Using the Lorenz time series and temperature data as examples, our work demonstrates how emergent phenomena enhance the capability of noisy many-body quantum systems for data processing and forecasting.
Quantum many-body systems near phase transitions respond collectively to externally applied perturbations. We explore this phenomenon in a laser-driven dissipative Rydberg gas that is tuned to a bistable regime. Here two metastable phases coexist, which feature a low and high density of Rydberg atoms, respectively. The ensuing collective dynamics, which we monitor , is characterized by stochastic collective jumps between these two macroscopically distinct many-body phases. We show that the statistics of these jumps can be controlled using a dual-tone microwave field. In particular, we find that the distribution of jump times develops peaks corresponding to subharmonics of the relative microwave detuning. Our study demonstrates the control of collective statistical properties of dissipative quantum many-body systems without the necessity of fine-tuning or of ultracold temperatures. Such robust many-body phenomena may find technological applications in sensing. Published by the American Physical Society 2024
Rydberg atoms, characterized by their strong and long-range dipole-dipole interactions, provide a versatile platform for exploring intriguing collective and many-body effects. Recently, the experimental realization of these effects in dense ensembles and reconfigurable atomic arrays has attracted significant interest, particularly for applications in quantum simulations and non-equilibrium physics. This review focuses on such recent development, discussing the theoretical foundations of the interactions between Rydberg atoms and the ensuing many-body physics, while providing a critical survey of experimental techniques for their precise manipulation and observation. We further discuss recent breakthroughs in leveraging Rydberg collective effects to probe novel many-body phases and non-equilibrium dynamics of these systems. By synthesizing theoretical insights with experimental milestones, we provide a comprehensive perspective on this rapidly evolving field and its transformative potential for future quantum technologies.
Abstract Far-from equilibrium dynamics that lead to self-organization are highly relevant to complex dynamical systems not only in physics, but also in life-, earth-, and social sciences. It is challenging however to find systems with sufficiently controllable parameters that allow quantitatively modelling of emergent properties. Here, we study a non-equilibrium phase transition and observe signatures of self-organized criticality in a dilute thermal vapour of atoms optically excited to strongly interacting Rydberg states. Electromagnetically induced transparency (EIT) provides excellent control over the population dynamics and enables high-resolution probing of the driven-dissipative dynamics, which also exhibits phase bistability. Increased sensitivity compared to previous work allows us to reconstruct the complete phase diagram including in the vicinity of the critical point. We observe that interaction-induced energy shifts and enhanced decay only occur in one of the phases above a critical Rydberg population. This limits the application of generic mean-field models, however a modified, threshold-dependent approach is in qualitative agreement with experimental data. Near threshold, we observe self-organized dynamics in the form of population jumps that return the density to a critical value.
Interacting many-body systems display enhanced sensitivity close to critical transition points due to diverging quantum fluctuations. This criticality-based enhancement has been suggested as a potential resource for applications in precision metrology. Here we demonstrate many-body critical enhanced metrology for the sensing of external microwave electric fields in a non-equilibrium Rydberg atomic gas. We show that small variations in external driving lead to a large variation in the population of Rydberg states around criticality and to a notable change in the optical transmission signal. For continuous optical transmission at the critical point, we quantify the enhanced sensitivity extracting the Fisher information, which shows a three orders of magnitude increase due to many-body effects compared with single-particle systems. These results demonstrate that critical properties of many-body systems are promising resources for sensing and metrology applications. Interacting quantum systems near criticality have been proposed as potential probes for quantum metrology. An experiment with Rydberg atoms now proves the enhanced sensitivity of critical many-body systems to small variations in external parameters.
This thesis reports the investigation of cooperative non-equilibrium dynamics in a thermal Rydberg ensemble. Cooperative behaviour arises due to resonant dipole-dipole interactions between highly excited Rydberg atoms. In order to transfer atomic population from the ground state to the Rydberg state in a caesium vapour, a three-photon excitation scheme is developed. This scheme has a number of benefits over traditional two-photon Rydberg excitation as each transition utilises in- expensive high-power diode lasers. The process of developing the excitation scheme produces a number of important results, including an excited-state polarisation spectroscopy technique and the observation of coherent three-photon electromagnetically induced transparency. The optical response and atomic dynamics of the interacting ensemble can be separated into two distinct phases. When the Rydberg number density is low and the interactions are negligible, the system can be described by the behaviour of a single atom. However, when the Rydberg number density is high, resonant dipole-dipole interactions result in a significant modification of the ensemble properties. This cooperative many-body phase cannot be described by the behaviour of a single atom. In the frequency domain, the interactions produce an excitation-dependent cooperative energy shift that is observed using probe transmission spectroscopy. In the time domain, the interactions result in a cooperative enhancement of the atomic decay rate that is analysed using fluorescence spectroscopy. At the transition between the single-body and many-body phase, a first-order non-equilibrium phase transition occurs. This is observed spatially along the length of the excitation region as a sharp switch in the emitted fluorescence. The first-order phase transition is also observed in the temporal response of the ensemble through critical slowing down. The divergence of the switching time to steady state follows a universal scaling law for phase transitions and the determined critical exponent is in excellent agreement with previous work on non-equilibrium phase transitions.
Understanding the collective quantum dynamics of non-equilibrium many-body systems is an outstanding challenge in quantum science. In particular, dynamics driven by quantum fluctuations are important for the formation of exotic quantum phases of matter1, fundamental high-energy processes2, quantum metrology3,4 and quantum algorithms5. Here we use a programmable quantum simulator based on Rydberg atom arrays to experimentally study collective dynamics across a (2+1)-dimensional Ising quantum phase transition. After crossing the quantum critical point, we observe a gradual growth of correlations through coarsening of antiferromagnetically ordered domains6. By deterministically preparing and following the evolution of ordered domains, we show that the coarsening is driven by the curvature of domain boundaries, and find that the dynamics accelerate with proximity to the quantum critical point. We quantitatively explore these phenomena and further observe long-lived oscillations of the order parameter, corresponding to an amplitude (‘Higgs’) mode7. These observations offer a viewpoint into emergent collective dynamics in strongly correlated quantum systems and non-equilibrium quantum processes. A programmable quantum simulator based on Rydberg atom arrays is used to study the collective dynamics of a quantum phase transition and observe the phenomenon of quantum coarsening.