发表机构
Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento; INFN-TIFPA, Trento Institute for Fundamental Physics and Applications; Department of Physics, Indian Institute of Technology Madras; Center for Quantum Information, Computation and Communication, Indian Institute of Technology Madras（特伦托大学物理系; 特伦托基础物理与应用研究所; 印度马德拉斯理工学院物理系; 印度马德拉斯理工学院量子信息、计算与通信中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出利用非KAM系统的共振敏感性作为量子传感器，通过计算量子费舍尔信息，发现其在满足共振条件时QFI显著增强，可实现优于混沌辅助等传感的计量性能。
AI 中文摘要
当受到弱时变扰动时，非KAM（柯尔莫哥洛夫-阿诺德-莫泽）系统会通过不变相空间环面的破裂，发生向经典混沌的突变。我们展示了非KAM系统在量子区域中作为量子传感器的应用，利用其在共振处的敏感性。量子费舍尔信息（QFI）是量子参数估计理论中的核心量，用于衡量量子态对编码于其中的未知参数所包含的信息量，即量化量子态对该参数微小变化的敏感性。本研究通过数值分析结合解析结果，计算QFI以探究非KAM系统在量子传感应用中的性能。我们发现，当满足共振条件时，QFI的增长会显著增强。对于弗洛凯幺正编码下的频率估计，我们推导得到一个输运界：若平均激发数增长为⟨n̂(t)⟩∼t^α，则QFI满足I(t)≲t^(2α+2)。量子受迫谐振子作为典型的非KAM系统，实现了完整的层级：局域动力学（α=0）产生二次增长，沿随机网的离域扩散（α=1）产生四次增长，而平移不变共振（α=2）则达到界的饱和，呈现反常六次增长I(t)∼t^6，该结果在共振R=2处通过解析得到，在R=4处通过数值得到。这种增强源于共振诱导的平移对称性，而非指数不稳定性，这表明非KAM共振是一种计量资源，与基于混沌辅助和临界性的传感不同。
英文摘要
Non-KAM (Kolmogorov-Arnold-Moser) systems, when subjected to weak time-dependent perturbations, exhibit an abrupt transition to classical chaos through the breakdown of invariant phase-space tori. We showcase the utilization of non-KAM systems in the quantum regime as quantum sensors, leveraging their sensitivity at \textit{resonances}. Quantum Fisher information (QFI) is a central quantity in quantum parameter estimation theory that measures how much information a quantum state contains about an unknown parameter that is encoded into it. In other words, it quantifies the sensitivity of a quantum state to small changes in that parameter. In this work, through numerical analysis in conjunction with analytical results, we study the performance of the non-KAM systems for quantum sensing applications by computing the QFI. We find that the growth of the QFI is remarkably enhanced when the resonance condition is satisfied. For frequency estimation under Floquet unitary encodings, we derive a transport bound: if the mean excitation number grows as $\langle\hat n(t)\rangle\sim t^α$, the QFI obeys $I(t)\lesssim t^{2α+2}$. The quantum kicked harmonic oscillator, a paradigmatic non-KAM system, realizes the full hierarchy: localized dynamics ($α=0$) yield quadratic growth, delocalized diffusion along stochastic webs ($α=1$) yields quartic growth, and translationally invariant resonances ($α=2$) saturate the bound with anomalous hexic growth, $I(t)\sim t^{6}$, established analytically at resonance $R=2$ and numerically at $R=4$. The enhancement stems from resonance-induced translational symmetry rather than exponential instability, identifying non-KAM resonances as a metrological resource distinct from chaos-assisted and criticality-based sensing.
Comments11+2 pages, 7 figures, This work builds in part on results presented in the doctoral thesis of one of the authors [arXiv:2409.10182]
