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Hierarchical quantum sensing with Floquet-engineered chaos and exceptional surfaces

Stella Rolande Mbokop Tchounda, Carolle Tchodimou, Philippe Djorwé, Sifeu Takougang Kingni, S. G. Nana Engo

Published Mar 31, 2026• 0 citations
Publisher

Abstract

Abstract 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.

DOI
10.21203/rs.3.rs-9170592/v1

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Abstract 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∝e2λmax⁡tS \propto e^{2\lambda_{\max} t}S∝e2λmax​t, providing a 100×100\times100× gain over the standard quantum limit and outperforming EP-based enhancement (12.5×12.5\times12.5×) for transient signals. The physical mechanism is a "Petermann bifurcation," where the non-orthogonality of Floquet modes (K≫1K \gg 1K≫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.
Within a normalized six-dimensional model of dissipative optomechanics (one cavity + two mechanical resonators), a synthetic-flux phase ΦsynΦ_{\rm syn}Φsyn​ acts as a reproducible control coordinate that selects the \emph{order} of a drive- and coupling-gated hyperchaos transition---up to four simultaneously positive Lyapunov exponents, beyond any reported single-mode benchmark. A phase-consistent Floquet--Lyapunov protocol (cross-checked by monodromy multipliers, dissipative volume balance ∑λi=Tr⁡(J)=−1.04\sumλ_i=\operatorname{Tr}(J)=-1.04∑λi​=Tr(J)=−1.04 and a 180-run three-seed audit) localizes the onset to a Neimark--Sacker bifurcation at $E^{*}=\num{1.060}$ (θ=0θ=0θ=0). As a secondary, model-level geometric clarification, the identical matched-resource force-sensing protocol returns a null gain on the chaotic attractor ($\mathcal{G}_{A/B}=\num{1.039}\pm\num{0.014}$), consistent with the matched-Fisher lemma: noise projected onto an unstable manifold is stretched by the same factor eλte^{λt}eλt as the deterministic signal. Truncated-Fock and truncated-Wigner checks support the mean-field description at selected points. All results remain strictly model-level: the strong-coupling sector lies $\num{2542}\times$ beyond anchored silicon optomechanical couplings. Closing that gap requires ultrasonic characterization of the mechanical degeneracy ω2ω_2ω2​, a measured inter-resonator hopping JmJ_mJm​, and the emergence of a genuine gigahertz platform.
We investigate the spectral structure of reset-driven Floquet quantum channels generated by the Hamiltonian evolution of a many-body system followed by periodic resetting of a bath. By tuning a perturbation parameter in the interacting Aubry-André-Harper(AAH) model, we find that exceptional points could emerge in the spectral transition from a symmetry-constrained ergodic regime to a fully chaotic regime. Across this transition, increasing the perturbation causes the real eigenvalues of the channel to drift, coalesce at exceptional points, and bifurcate into complex-conjugate pairs, reflecting the progressive breaking of symmetry constraints in operator space. We further show that the channel spectrum sharply distinguishes chaotic, ergodic, many-body localized, and scarred dynamical regimes. Finally, we connect the leading channel eigenvalues to experimentally accessible probes based on quantum mutual information, establishing a link between the spectral organization of reset-driven quantum channels and observable relaxation dynamics. We implement the protocol on the IBM Quantum Platform and verify that the dynamical differences are reflected in the decay of mutual information.
Exceptional points (EPs) can induce strongly amplified responses to weak perturbations, but enhanced spectral sensitivity in conventional non-Hermitian systems does not necessarily translate into improved quantum-limited sensing because of the associated gain and loss noise. Here, we investigate a tunable EP sensing platform based on the intrinsic non-Hermitian Bogoliubov dynamics of a spin-orbit-angular-momentum-coupled Bose-Einstein condensate. Starting from a fully Hermitian microscopic Hamiltonian, we derive a Bogoliubov dynamical matrix that exhibits parity-time (PT) symmetry, with EPs tunable through the Raman coupling and interaction parameters. We identify multiple EPs and map their trajectories and associated stability landscapes, revealing strong quantum Fisher information enhancement when the EPs are approached from the PT-symmetric stable regime. We further find that the gap-opening rate around a second-order EP provides a useful relative indicator for comparing the sensing performance of EPs, while higher-order EPs are not necessarily accessible from the stable regime. Moreover, two second-order EPs can be tuned to overlap, allowing their sensing contributions to add and yielding a linear enhancement of the total quantum Fisher information. Finally, we show that a spin-density measurement can approach the quantum Fisher information limit, providing an experimentally accessible route to tunable EP-enhanced quantum sensing in Bose-Einstein condensates.
Subjecting a physical system to a time-periodic drive can substantially modify its properties and applications. This Floquet-engineering approach has been extensively applied to a wide range of classical and quantum settings in view of designing synthetic systems with exotic properties. Considering a general class of two-mode nonlinear optical devices, we show that effective optical nonlinearities can be created by subjecting the light field to a repeated pulse sequence, which couples the two modes in a fast and time-periodic manner. The strength of these drive-induced optical nonlinearities, which include an emerging four-wave mixing, can be varied by simply adjusting the pulse sequence. This leads to topological changes in the system's phase space, which can be detected through light intensity and phase measurements. Our proposal builds on an effective-Hamiltonian approach, which derives from a parent quantum many-body Hamiltonian describing driven interacting bosons. As a corollary, our results equally apply to Bose-Einstein condensates in driven double-well potentials, where pair tunneling effectively arises from the periodic pulse sequence. Our scheme offers a practical route to engineer and finely tune exotic nonlinearities and interactions in photonics and ultracold quantum gases.
Open photonic systems provide a versatile platform for non-Hermitian physics, enabling control over complex spectra, transport, and light-matter interactions. Exceptional points (EPs), at which eigenvalues and eigenvectors coalesce and the governing operator becomes defective, play a central role because they combine branch-point spectral topology, nonanalytic perturbative response, and controllable eigenstate conversion. This Review provides a unified framework for EP photonics by systematically distinguishing exceptional degeneracies according to the underlying operator, spectral variable, boundary conditions, and experimentally accessible observables. We discuss Hamiltonian EPs, absorbing EPs associated with scattering zeros, real-frequency scattering-matrix and Jones-matrix EPs, Bloch and Floquet EPs, and Liouvillian EPs in open quantum systems. We review their spectral topology, static and dynamical encircling, higher-order exceptional structures, and coexistence with bound states in the continuum, together with applications in sensing, lasing, coherent absorption, directional scattering, polarization and wavefront control, nonlinear optics, optical storage, nonreciprocal photonics, and quantum photonics. We also critically assess the current limitations, practical challenges, and future perspectives of EP-based photonic technologies, with particular attention to robustness, noise, scalability, and experimentally measurable performance.