引力谐波琴：谐和陷阱中引力诱导的纠缠
Gravitational Harmonium: Gravitationally Induced Entanglement in a Harmonic Trap
AI总结：
提出“引力谐波琴”思想实验，通过非相对论量子力学分析三维谐和陷阱中两粒子经引力相互作用产生的纠缠，为后续量子场论建模和相对论修正研究奠定基础。
摘要：
近期研究表明，在不久的将来，桌面实验可能有望探测到引力诱导的纠缠。然而，目前尚无针对此类实验的成熟模型，即在这种模型中，纠缠粒子被更基础地视为相对论性量子场的激发态，且测量通过场可观测量的期望值来建模。在此，我们提出一个思想实验：两个粒子（即有质量标量场量子）初始被制备为共同的三维（3D）谐和陷阱中相干态的叠加。随后，粒子通过彼此间的引力相互作用产生纠缠，这一过程可通过粒子位置探测概率来探测。本文对该系统的引力诱导纠缠进行了非相对论量子力学分析；由于其类似于氦原子中近似电子相互作用的谐波琴模型，我们将其称为“引力谐波琴”；纠缠通过物质波干涉可见度在操作上加以确定。本文为后续研究奠定基础，后续研究将使用量子场论对该系统建模，通过相对论修正进一步揭示引力诱导纠缠的量子本质，并提供量化纠缠的操作程序。
英文摘要：
Recent work has shown that it may be possible to detect gravitationally induced entanglement in tabletop experiments in the not-too-distant future. However, there are at present no thoroughly developed models for this type of experiment where the entangled particles are treated more fundamentally as excitations of a relativistic quantum field, and with the measurements modeled using expectation values of field observables. Here we propose a thought experiment where two particles (i.e., massive scalar field quanta) are initially prepared in a superposition of coherent states within a common three-dimensional (3D) harmonic trap. The particles then develop entanglement through their mutual gravitational interaction, which can be probed through particle position detection probabilities. The present work gives a non-relativistic quantum mechanical analysis of the gravitationally induced entanglement of this system, which we term the `gravitational harmonium' due to its similarity to the harmonium model of approximate electron interactions in a helium atom; the entanglement is operationally determined through the matter wave interference visibility. The present work serves as the basis for a subsequent investigation, which models this system using quantum field theory, providing further insights into the quantum nature of gravitationally induced entanglement through relativistic corrections, together with an operational procedure to quantify the entanglement.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
