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<p>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<sup>−1</sup>, and partial energy recurrences–phenomena strongly reminiscent of the Fermi-Pasta-Ulam-Tsingou physics. We observe dissipation rates below 4&#xa0;×&#xa0;10<sup>−6</sup> Hz, limited by our ability to measure dissipation in presence of nonlinear dynamics. We estimate an intrinsic acceleration sensitivity of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(62\times 1{0}^{-12}\,g/\sqrt{Hz}\)</EquationSource> <EquationSource Format="MATHML"><math> <mn>62</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>12</mn> </mrow> </msup> <mspace width="0.25em" /> <mi>g</mi> <mo>/</mo> <msqrt> <mrow> <mi>H</mi> <mi>z</mi> </mrow> </msqrt> </math></EquationSource> </InlineEquation>, 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.</p>

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Nonlinear dynamics and Fermi-Pasta-Ulam-Tsingou recurrences in macroscopic ultra-low loss levitation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月19日

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  • Mehrdad Malekian Sourki,
  • Wisdom Boinde,
  • Ali Najjar Amiri,
  • Mahdi Hosseini

摘要

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 × 10−6 Hz, limited by our ability to measure dissipation in presence of nonlinear dynamics. We estimate an intrinsic acceleration sensitivity of \(62\times 1{0}^{-12}\,g/\sqrt{Hz}\) 62 × 1 0 − 12 g / H z , 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.