可调阶希尔伯特空间遍历性的实验研究
Experimental Investigation of Tunable-Order Hilbert-Space Ergodicity
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中文总结 AI 辅助
本研究提出m音驱动实现k-HSE的方案，经金刚石氮空位中心实验验证，揭示有限阶HSE的初始状态依赖性，拓展了量子遍历性研究。
中文摘要 AI 辅助
希尔伯特空间遍历性（HSE）为研究受驱动量子系统的热化提供了新框架，补充了仅适用于静态系统的本征态热化假设。该遍历性具有层级性：通过量化动力学在希尔伯特空间中探索的随机性，可得到一系列称为k-HSE的层级。尽管HSE已在最低和最高层级被观测到，但由于难以构造此类驱动，有限阶HSE动力学仍未被充分探索。本文研究该中间区域并揭示其独特物理特性：首先提出并证明，量子比特上的m音驱动可实现阶数不超过k=2m-3的k-HSE，驱动参数的确定代价为O(k)；利用金刚石中的单个氮空位中心，我们验证了该设计，表明3音驱动可实现3-HSE，其四阶统计量依赖于初始状态。进一步的深入理论分析显示，该初始状态依赖性在所有驱动中普遍存在，证明即使动力学是遍历的，也可通过高阶统计量恢复初始状态。本研究拓展了量子遍历性的研究，并揭示了其层级内的有趣物理特性。
英文摘要
Hilbert-space ergodicity (HSE) provides a new framework for studying thermalization in driven quantum systems, complementing the eigenstate thermalization hypothesis, which is restricted to static systems. This ergodicity is hierarchical: by quantifying how randomly the dynamics explores the Hilbert space, one obtains a family of levels termed $k$-HSE. While HSE has been observed at the lowest and highest levels, finite-order HSE dynamics remains largely unexplored due to the difficulty of constructing such drives. Here, we explore this intermediate regime and uncover its distinctive physics. We first propose and prove that a family of $m$-tone drives on qubits realizes $k$-HSE up to $k = 2m{-}3$, with drive parameters determined at $O(k)$ cost. Using a single nitrogen-vacancy center in diamond, we verify this design by showing that a 3-tone drive realizes 3-HSE, with fourth-order statistics depending on the initial state. Further in-depth theoretical analysis shows that this initial-state dependence is generic across drives, demonstrating the possibility of recovering the initial state from higher-order statistics even when the dynamics is ergodic. Our work broadens the study of quantum ergodicity and reveals intriguing physics within its hierarchy.
