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arXiv:2510.13218 · Physical Review A

Observation of nonlinear spin dynamics in dual-cell atomic gases

Xiaofan Wang, Haitao Lu, Hengyan Wang, Zhihuang Luo, Wenqiang Zheng

Published Jun 9, 2026• 0 citations
arXivHTMLPDF

Abstract

Nonlinear spin systems exhibit rich and exotic dynamical phenomena, offering promising applications ranging from spin masers and time crystals to precision measurement. Recent theoretical work [T. Wang et al., Commun. Phys. 8, 41 (2025)] predicted intriguing nonlinear dynamical phases arising from inhomogeneous magnetic fields and feedback interactions. However, experimental exploration of these predictions remains lacking. Here, we report the observation of nonlinear spin dynamics in dual-bias magnetic fields with dual-cell alkali-metal atomic gases and present three representative stable dynamical behaviors of limit cycles, quasi-periodic orbits, and chaos. Additionally, we probe the nonlinear phase transitions between these phases by varying the feedback gain and the difference of dual-bias magnetic fields. Furthermore, we demonstrate the robustness of the limit cycle and quasi-periodic orbit against the noise of magnetic fields. Our findings establish a versatile platform for exploring complex spin dynamics and open new avenues for the realization of multimode spin masers, time crystals and quasi-crystals, and high-precision magnetometers.

DOI
10.1103/k1hd-p6np

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Nonlinear spin systems exhibit rich and exotic dynamical phenomena, offering promising applications ranging from spin masers and time crystals to precision measurement. Recent theoretical work [T. Wang et al., Commun. Phys. 8, 41 (2025)] predicted intriguing nonlinear dynamical phases arising from inhomogeneous magnetic fields and feedback interactions. However, experimental exploration of these predictions remains lacking. Here, we report the observation of nonlinear spin dynamics in dual-bias magnetic fields with dual-cell alkali-metal atomic gases and present three representative stable dynamical behaviors of limit cycles, quasi-periodic orbits, and chaos. Additionally, we probe the nonlinear phase transitions between these phases by varying the feedback gain and the difference of dual-bias magnetic fields. Furthermore, we demonstrate the robustness of the limit cycle and quasi-periodic orbit against the noise of magnetic fields. Our findings establish a versatile platform for exploring complex spin dynamics and open new avenues for the realization of multimode spin masers, time crystals and quasi-crystals, and high-precision magnetometers.
Nonlinear spin dynamics are essential in exploring nonequilibrium quantum phenomena and have broad applications in precision measurement. Among these systems, the combination of a bias magnetic field and feedback mechanisms can induce self-sustained oscillations at the base Larmor frequency due to nonlinearity. These features have driven the development of single-species and multiple-species spin masers. The latter, with multiple discrete Larmor frequencies, provides significant advantages for precision measurement by mitigating uncertainties in precession frequencies due to long-term drifts in experimental conditions. The self-sustained oscillations of single-species and multiple-species spin masers correspond to limit cycles and quasi-periodic orbits of the stable nonlinear dynamics of the systems, respectively; the correspondence is elucidated in a recent study on a related spin system featuring two discrete intrinsic Larmor frequencies under dual bias magnetic fields [T. Wang et al., Commun. Phys. 8, 41 (2025)]. Here, we extend the study to the case where the intrinsic Larmor frequencies of individual spins of the system, given rise to by an inhomogeneous bias magnetic field, form a continuum. We show that generically the stable dynamics of the system includes limit cycles, quasi-periodic orbits, and chaos. We establish the relation between the synchronization frequency of limit cycles and the field inhomogeneity and derive an equation determining the stability of limit cycles. Furthermore, detailed characteristics of different dynamical phases, especially the robustness of limit cycles and quasi-periodic orbits against experimental fluctuations, are discussed. Our findings not only encompass the case of discrete Larmor frequencies, but also provide crucial insights for precision measurement and the exploration of continuous time crystals and quasi-crystals.
Continuous time crystals (CTCs) are a phase of matter characterized by spontaneous breaking of continuous time-translation symmetry. Recently, CTCs have garnered interest due to breakthroughs in experimental implementation. Here we report the experimental observation of CTCs in noble-gas nuclear spins and uncover previously unexplored dynamical phenomena. We observe that the CTCs manifest as persistent limit cycle oscillations of nuclear spins, with coherence times exceeding hours. Notably, these oscillations are robust against noise perturbations and exhibit random time phases upon repetitive realization, epitomizing continuous time-translation symmetry-breaking intrinsic to CTCs. Additionally, we observe a dynamical phase featuring quasi-periodic oscillations and random time phases, indicating the emergence of the continuous time quasi-crystals proposed by recent theories. By varying the feedback strength and magnetic gradient, we observe complex dynamical phase transitions between time crystal phases and chaotic regimes. This work broadens the catalog of phases of spin gases and unlocks opportunities in precision measurements. The authors report on the observation of continuous time crystals of nuclear spins of 129Xe atoms within a Rb-Xe gaseous mixture in a magnetic feedback scheme. This unveils nontrivial role of magnetic fields and a new continuous time quasi-crystal phase.
Spin masers with optical detection and artificial feedback are widely used in fundamental and practical applications. However, a full picture of the maser dynamics is still absent. By solving the feedback-driven Bloch equations, we simulated the dynamics of an ideal spin maser in a broad parameter space. Rich nonlinear dynamics including high-order-harmonic generation, nonperiodic spin oscillations, and frequency comb were revealed when the artificial feedback interaction exceeds the normal spin-field interaction. We also propose a pulse feedback spin maser protocol, which constructs an ultralow field magnetic frequency comb and could be useful in precision atomic magnetometers in searching for spin-dependent exotic interactions.
Abstract Non-equilibrium phase transitions are a vibrant frontier in physics, driving breakthroughs across diverse disciplines in recent years. Thermal spin ensembles, a captivating many-body quantum system, have harnessed their collective strengths to set remarkable measurement benchmarks in equilibrium. However, their non-equilibrium dynamics remain unexplored, with nonlinear interactions among constituents offering a rich playground for phase transition studies. Here, we employ nonlinear magnetic feedback to achieve real-time observation and control of phase transitions in a driven-dissipative spin ensemble, unveiling dynamic shifts between limit cycles, subharmonics, and chaos. This work not only deepens our grasp of critical phenomena in non-equilibrium systems but also paves the way for chaos-based sensing and information processing technologies, bridging fundamental physics with transformative applications.
We have completed a thorough study of masing action of hyperpolarized He-3 gas in inhomogeneous magnetic fields. The self interaction of the He-3 magnetization has a large effect on the maser gain. We have developed a simple new magnetic resonance method for investigating the interactions of Xe-129 spins with protons in polymers. We have shown that there are novel magnetic resonance transitions in alkali-metal vapors that have vanishing spin-exchange broadening in the limit of high spin polarization. Such transitions could be useful for miniaturized atomic clocks. We have shown that spin-axis interactions in triplet molecules are responsible for much of the spin destruction rate dense alkali-metal vapors.
With the state-of-the-art quantum measurement devices, such as atomic clocks, atomic gyroscopes, and atomic magnetometers, as their central components, the spatiotemporal evolution of atomic spin polarization in the atomic vapor cell has a major effect on both increasing the bandwidth of magnetometer and improving the accuracy of magnetic gradient measurements. However, the major factor impeding the further improvement of the performance of quantum measurement instrument is the inherent static nature of the traditional intra-vapor cell segmentation imaging technique, which makes it challenging to achieve the real-time capture of the dynamic evolution of atomic spin states. In this work, we suggest a dynamic spin imaging method for alkali metal atomic vapor cells with real-time modification of atomic spin polarization states in order to overcome this technological difficulty. In particular, to ensure that the laser can precisely act on the alkali metal atoms in various regions in the vapor cell, we employ a complex beam array management system to modify the on/off state of the laser beams at various positions in the spatial dimension in real time. In the meantime, we generate laser fields with particular spatial distribution and frequency characteristics by using frequency modulation techniques in the time series to accurately regulate the on-off frequency of each laser beam in the beam array. These laser beams cause dynamic changes in the atomic spin polarization state by interacting with alkali metal atoms at various points in the vapor cell. Through precise adjustment of the laser properties, we can see and study the dynamic evolution of the atomic spin-polarization state in real time. According to the experimental data, the technology outperforms the traditional static spin imaging techniques by achieving an excellent temporal resolution of 355 frames per second and a spatial resolution of 95.9 micrometers. The effective use of this method enables us to monitor and evaluate the dynamic aspects of magnetic field distribution with unprecedented precision, also greatly enhance our understanding of the dynamic characteristics of atomic spin polarization.