Observation of Nonlinear Spin Dynamics in Dual-Cell Atomic Gases

TL;DR

This work experimentally demonstrates nonlinear spin dynamics in a dual-cell, feedback-driven alkali-atom system with distinct static fields, revealing synchronized limit cycles, quasi-periodic oscillations, and chaos as the dual-bias difference and feedback gain are varied. The authors implement a dual-vapor-cell rubidium magnetometer where a common feedback field couples two ensembles with different Larmor frequencies, and they map a phase diagram in terms of $\Delta\omega$ and $1/R$. They verify phase characteristics through time traces, spectra, and a chaos-detection metric, and show robustness to magnetic-field noise, highlighting potential for multimode spin masers and time/quasi-crystal applications along with high-precision magnetometry. The results provide a versatile platform for exploring complex nonlinear spin dynamics and advancing practical quantum technologies in realistic environments.

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.

Figures (5)

• Figure 1: Experimental setup of the dual-cell self-oscillating magnetometer. The detected probe signal is fed back through coils as $B_{\text{ref}}$ to sustain spin precession and generate nonlinear dynamics. Optical components are labeled as follows: PBS (polarizing beam splitter); M (mirror); CL (convex lens); $\frac{1}{2}\lambda$ and $\frac{1}{4}\lambda$ (half- and quarter-wave plates). The coordinate axes $(x,y,z)$ indicate the laboratory reference frame.
• Figure 2: Representative trajectories of the average spin polarization $\{\overline{M}_x, \overline{M}_y, \overline{M}_z\}$ in three dynamical phase regimes: (a) limit cycle, (b) quasi-periodic orbit, and (c) chaos. Blue dots denote the simulated trajectories, while red markers highlight the corresponding Poincaré sections.
• Figure 3: Experimental results. Time traces and Fourier spectra showing limit-cycle (a,b), quasi-periodic (c,d), and chaotic (e,f) dynamics of the dual-cell self-oscillating system.
• Figure 4: Experimental phase diagram of the dual-cell system showing regions of no signal, limit cycle (blue), quasi-periodic (purple), and chaotic (orange) dynamics as functions of $\Delta\omega$ and feedback strength $1/R$.
• Figure 5: Noise robustness of limit-cycle and quasi-periodic dynamical regimes. (a) Normalized noise-resistance parameter Q as a function of noise strength. (b) and (c) show the Fourier spectra without and with white noise added. The added noise strength is $2$ V.