腔量子电动力学中高阶集体自旋相互作用的分析理论
Analytical Theory of Higher-Order Collective Spin Interactions in Cavity Quantum Electrodynamics
AI总结：
本文推导了腔介导集体自旋相互作用完整层级的闭式解析表达式，明确了高阶非线性系数的规律，为研究高阶非线性在集体纠缠与量子增强传感中的作用提供了通用框架。
AI中文摘要：
腔介导的集体自旋相互作用通常由二次单轴扭曲哈密顿量描述，但底层的原子-光相互作用会自然产生任意阶的非线性项。本文推导了腔介导集体自旋相互作用完整层级的闭式解析表达式，证明非线性系数χ_k由切比雪夫多项式决定（k为非线性阶数），得到其与单原子合作度η满足χ_k∝η^k的普适标度关系，以及系数对腔失谐的依赖关系。该结果提供了确定高阶非线性何时起作用、二次近似何时失效的系统框架，明确了高阶项显著改变集体自旋动力学的实验相关区域，可加速量子关联与量子费舍尔信息的产生，有限阶展开能准确复现完整腔介导演化。研究为理解腔量子电动力学中的高阶非线性及其在集体纠缠与量子增强传感中的作用建立了通用框架。
英文摘要：
Cavity-mediated collective-spin interactions are commonly described by a quadratic one-axis twisting Hamiltonian. However, the underlying atom-light interaction naturally generates nonlinearities to arbitrary order. Here, we derive a closed-form analytical expression for the complete hierarchy of cavity-mediated collective-spin interactions. We show that the nonlinear coefficients $χ_k$ are governed by Chebyshev polynomials, with $k$ the order of nonlinearity. This yields a universal scaling $χ_k\proptoη^k$ with the single-atom cooperativity $η$ and a description of their dependence on cavity detuning. The result provides a systematic framework for determining when higher-order nonlinearities become relevant and when the quadratic approximation breaks down. We identify experimentally relevant regimes in which higher-order terms substantially modify collective-spin dynamics, accelerating the generation of quantum correlations and quantum Fisher information, and demonstrate that finite-order expansions can accurately reproduce the full cavity-mediated evolution. Our results establish a general framework for understanding higher-order nonlinearities in cavity quantum electrodynamics and their role in collective entanglement and quantum-enhanced sensing.
