Nonlinear Dynamics and Fermi-Pasta-Ulam-Tsingou Recurrences in Macroscopic Ultra-low Loss Levitation

Abstract

Macroscopic systems, when governed by nonlinear interactions, can display rich behavior from persistent oscillations to signatures of ergodicity breaking. Nonlinearity, long regarded as a nuisance in precision systems, is increasingly recognized as a gateway to new physical regimes. While such dynamics have been extensively studied in optics and atomic physics, macroscopic systems are rarely associated with long-lived coherence and nonlinear control and remain an untapped platform for probing the fundamental nonlinear processes. Here, we report the observation of long-lived oscillatory dynamics in millimeter-scale levitated dielectric quartz particles exhibiting clear signatures of nonlinear mode coupling, a positive largest Lyapunov exponent of 0.0095 s^-1, and partial energy recurrences-phenomena strongly reminiscent of the Fermi-Pasta-Ulam-Tsingou physics. We observe dissipation rates below 4*10E-6 Hz, limited by our ability to measure dissipation in presence of nonlinear dynamics. We estimate an intrinsic acceleration sensitivity of 62*10E-12 g/sqrt(Hz), at room temperature. The magnetic trap is constructed from a static arrangement of permanent magnets, requiring no external power or active feedback. Our findings open a path toward leveraging nonlinear dynamics for novel applications in sensing, signal processing, and statistical mechanics.