发表机构
Universidad Autónoma de Chihuahua; University of Hohenheim; Universidad Autónoma Metropolitana–Cuajimalpa（奇瓦瓦自治大学; 霍恩海姆大学; 自治都市大学-夸希马尔帕校区）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究精确求解耦合参变振荡器的高斯纠缠动力学，揭示对数负性由单一不变量决定，并证明初始宽度与啁啾可作为纠缠的独立实验控制手段。
AI 中文摘要
我们研究两个由共同含时弹簧驱动的双线性耦合谐振子。一个固定的简正模变换将这对谐振子约化为两个参变振荡器，每个都通过其Lewis-Riesenfeld不变量和Ermakov-Pinney振幅精确求解，包括阶梯算子构造和Lewis-Riesenfeld相位。对于不变量真空输入，物理双模协方差矩阵以闭式获得，对数负性简化为$E_{N}=\frac{1}{2} \operatorname{arcosh}(X/2)$，其中单个无量纲不变量$X \geq 2$度量两个简正模的相对相空间形变。我们给出了Duan--Simon比较的归一化显式描述：在局域辛优化后，Duan检验和正部分转置对此纯交换对称高斯族共享纠缠阈值，但优化后的Duan量是一个见证者，而非独立度量，且$D_{\rm opt}/D_{\rm sep}=e^{-E_N}$。我们仔细区分了真正可分离的乘积制备与耦合哈密顿量的已纠缠基态，并仅使用前者来声称纠缠产生。在正弦刚度调制下，可分离输入在远离共振时显示有界关联，在参变共振附近显示持续增长，我们数值证明初始宽度和啁啾在选定目标时刻充当纠缠的两个独立、实验可访问的控制。一个$SU(1,1)$表述将$2 E_{N}$识别为$SU(1,1)/U(1)$圆盘上两个简正模压缩轨迹的双曲分离，并表明纠缠由相对压缩幅度和相对压缩角度共同控制；我们展示了几乎相等的幅度仍可通过角度单独产生强纠缠的机制。
英文摘要
We study two bilinearly coupled harmonic oscillators driven by a common time-dependent spring. A fixed normal-mode transformation reduces the pair to two parametric oscillators, each solved exactly by its Lewis-Riesenfeld invariant and Ermakov-Pinney amplitude, including the ladder-operator construction and the Lewis-Riesenfeld phase. For invariant-vacuum inputs the physical two-mode covariance matrix is obtained in closed form, and the logarithmic negativity collapses to $E_{N}=\frac{1}{2} \operatorname{arcosh}(X/2)$, where a single dimensionless invariant $X \geq 2$ measures the relative phase-space deformation of the two normal modes. We give a normalization-explicit account of the Duan--Simon comparison: after local symplectic optimization the Duan test and the positive partial transpose share the entanglement threshold for this pure exchange-symmetric Gaussian family, but the optimized Duan quantity is a witness, not an independent measure, with $D_{\rm opt}/D_{\rm sep}=e^{-E_N}$. We carefully separate a genuinely separable product preparation from the already-entangled ground state of the coupled Hamiltonian, and use only the former for claims of entanglement generation. Under sinusoidal stiffness modulation a separable input shows bounded correlations away from resonance and sustained growth near parametric resonance, and we demonstrate numerically that the initial width and chirp act as two independent, experimentally accessible controls of the entanglement at a chosen target time. An $SU(1,1)$ formulation identifies $2 E_{N}$ with the hyperbolic separation of the two normal-mode squeezing trajectories on the $SU(1,1)/U(1)$ disk and shows that entanglement is governed by both the relative squeezing magnitude and the relative squeezing angle; ; we exhibit regimes in which nearly equal magnitudes still produce strong entanglement through the angle alone.
Comments7 figures, 16 pages
