发表机构
The University of Oklahoma; Oklahoma State University（俄克拉荷马大学; 俄克拉荷马州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种利用局域交换相互作用产生能隙保护，抑制非集体激发，从而在多能级自旋系统中实现海森堡极限压缩的通用机制，并适用于多种实验平台。
AI 中文摘要
我们展示了一种通用机制，可在具有幂律相互作用的多能级（qudit）自旋系统中产生可扩展的、计量学上有用的纠缠，形式为广义自旋压缩。我们针对自旋改变动力学展示了这一点，将自旋向列压缩的物理（已知于自旋-1玻色-爱因斯坦凝聚体）扩展到空间扩展的晶格几何。在没有全连接性的情况下，动力学通常会泄漏到非集体的有限动量模式中，从而破坏海森堡标度。我们表明，引入局域$\mathfrak{su}(D)$交换相互作用会建立一个能隙，保护完全对称的集体流形，抑制非集体激发，并在任何幂律指数下，在一到三维中实现海森堡标度$\xi^2\propto1/N$。我们通过分析Bogoliubov激发谱提供了对该机制的解析理解，并通过量子多体动力学的数值模拟展示了其有效性。我们的发现更广泛地适用于其他自旋压缩哈密顿量，并直接推广到更大的内部自旋维度。我们的结果为在实验平台（如（极性）分子阵列、磁性原子和里德伯原子）中实现多能级自旋系统，提供了通向可扩展的海森堡极限的qudit纠缠产生的实用途径。
英文摘要
We demonstrate a general mechanism to generate scalable, metrologically useful entanglement in the form of generalized spin squeezing in multi-level (qudit) spin systems with power-law interactions. We demonstrate this for spin-changing dynamics, extending the physics of spin-nematic squeezing known from spinor BECs to spatially extended lattice geometries. In the absence of all-to-all connectivity, the dynamics generally suffers from leakage into non-collective finite-momentum modes, destroying Heisenberg scaling. We show that introducing local $\mathfrak{su}(D)$ exchange interactions establishes an energy gap that protects the fully symmetric collective manifold, suppressing non-collective excitations, and achieving Heisenberg scaling $ξ^2\propto1/N$ in one to three dimensions for any power-law exponent. We provide an analytical understanding of the mechanism via the analysis of the Bogoliubov excitation spectrum, and demonstrate its effectiveness via numerical simulations of the quantum many-body dynamics. Our findings more broadly apply to other spin-squeezing Hamiltonians, and directly generalize to larger internal spin dimensions. Our results provide a practical pathway towards scalable Heisenberg-limited qudit entanglement generation in experimental platforms such as arrays of (polar) molecules, magnetic atoms, and Rydberg atoms realizing multi-level spin systems.
Comments12 pages + 4 main figures+ 5 supplemental figures
