发表机构
Institute for Theoretical Physics, Friedrich Schiller University Jena; Institute for Theoretical Physics, University of Amsterdam; Canadian Institute for Theoretical Astrophysics, University of Toronto（耶拿弗里德里希·席勒大学理论物理研究所; 阿姆斯特丹大学理论物理研究所; 多伦多大学加拿大理论天体物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究二次曲率引力中两个量子谐振子的引力诱导纠缠，推导有效哈密顿量，发现纠缠消失频率，并给出自旋-2与自旋-0鬼魅质量的约束条件，实验可区分低至0.0197 eV的自旋模式。
AI 中文摘要
我们研究了由二次（Stelle）引力诱导的两个量子谐振子之间的引力生成纠缠，修正项包含至1.5后牛顿阶。从二次作用量出发，我们推导了两个谐波束缚质量的等效两体哈密顿量，其中包含了引力场的巨质量自旋-2鬼魅（$m_2$）和巨质量自旋-0（$m_0$）自由度的贡献。对于制备在基态的两个量子化振子，我们计算了约化态的冯·诺依曼熵和Rényi熵，并确定了一个频率，在该频率下引力诱导的纠缠由于相对论动量压缩与量子非定域引起的位置压缩之间的抵消而消失。我们进一步分析了该抵消频率，并推导出自旋-2和自旋-0模式的近似约束$m_0 < \u221b[3]{4} m_2$。该关系源于要求稳定的谐振子描述。最后，我们研究了非高斯设置中引力诱导的并发度，并展示了二次引力如何修改两个空间叠加之间生成的纠缠。对于某些质量、空间叠加、粒子间距以及自旋-2和自旋-0模式的选择，并发度可以接近$\u039f(1)$。并发度将在某些粒子间距处偏离牛顿引力，这取决于自旋-2和自旋-0模式的能量。例如，低至0.0197 eV的自旋模式在距离$d \u223c 40 \u03bcm$处变得与牛顿引力可区分。这使我们能够在实验中约束自旋-2和自旋-0的质量。
英文摘要
We investigate gravitationally generated entanglement in two quantum harmonic oscillators induced by quadratic (Stelle) gravity, including corrections up to $1.5$ post-Newtonian order. Starting from the quadratic action, we derive the effective two-body Hamiltonian for two harmonically trapped masses, incorporating the contributions of the massive spin-$2$ ghost ($m_2$) and massive spin-$0$ ($m_0$) degrees of freedom of the gravitational field. For two quantised oscillators prepared in their ground state, we compute the von Neumann and Rényi entropies of the reduced state and identify a frequency at which the gravitationally-induced entanglement vanishes due to cancellation between relativistic momentum squeezing and quantum-delocalisation-induced position squeezing. We further analyze the cancellation frequency and derive the approximate constraint $m_0 < \sqrt[3]{4}\, m_2$ for the spin-$2$ and spin-$0$ modes. This relation follows from demanding a stable harmonic oscillator description. Finally, we study gravitationally-induced concurrence in a non-Gaussian setup and show how quadratic gravity modifies the entanglement generated between two spatial superpositions. The concurrence can approach $\mathcal{O}(1)$ for certain choices of mass, spatial superposition, particle distance, and spin-$2$ and spin-$0$ modes. The concurrence will deviate from Newtonian gravity at certain particle separations, depending on the energy of the spin-$2$ and spin-$0$ modes. For example, spin modes as low as $0.0197$ eV become distinguishable from Newtonian gravity at a distance $d \sim 40 μ$m. This allows us to constrain the spin-$2$ and spin-$0$ masses in experiments.
Comments15 pages + 6 pages appendix, 6 figures
