Hierarchical quantum sensing with Floquet-engineered chaos and exceptional surfaces

This Letter presents a hierarchical quantum sensing strategy in Floquet-engineered optomechanical systems based on the topological transition from limit cycles to strange attractors. Analyzing the global attractor landscape reveals three sensing regimes: linear operation, exceptional points (EPs), and high-order chaos. The chaotic regime yields a sensitivity scaling $S \propto e^{2\lambda_{\max} t}$, providing a $100\times$ gain over the standard quantum limit and outperforming EP-based enhancement ($12.5\times$) for transient signals. The physical mechanism is a "Petermann bifurcation," where the non-orthogonality of Floquet modes ($K \gg 1$) persists beyond the stability boundary, combining topological and dynamical amplification. Ultra-Strong Coupling (USC) effects significantly expand the chaotic basin, robustly preserving these gains against experimental disorder.