Unveiling the complexity of pulsation routes to chaos of spatiotemporal soliton molecules

Exploring three-dimensional (3D) soliton molecule dynamics holds great potential for unraveling the underlying mechanisms of molecular complexity and addressing unresolved challenges in nonlinear systems. However, real-time, high-fidelity visualization of their spatiotemporal evolution, especially chaotic transitions, has remained largely unexplored in the experiment, as achieving high-spatiotemporal-resolution and long-term observation is still challenging. Here, we report the first experimental observation of the intricate pulsation-to-chaos routes in 3D soliton molecules using a real-time multispeckle spectral-temporal measurement technique. Different trajectories from initial period-doubling to chaotic states are resolved under gain perturbation, spanning multiple-period bifurcation with intriguing radio-frequency sideband drift or soliton molecule dissociation, a regime previously uncharted for 3D soliton-pair molecules. The chaotic evolution of 3D soliton molecules is quantitatively verified by calculating Lyapunov exponents and correlation dimension analysis. Gain-induced nonlinear spatiotemporal coupling plays a vital role in these dynamic processes and further elucidated through numerical simulations. Our findings further extend the parallel analogy between 3D soliton molecules and matter molecules, providing new perspectives on nonlinear dynamics and potential applications in high-dimensional optical information processing.