Tabletop Tests of Quantum Gravity Non-Gaussianity: A Dual-Approach Study from Theoretical Benchmark to Exploratory Implementation

Experimental tests of quantum gravity have long been limited by the extreme energy scale of the Planck regime. In recent years, theoretical proposals for testing gravitational non-Gaussianity using tabletop quantum systems have made significant progress, but existing schemes face severe challenges in experimental feasibility: the BEC+Feshbach scheme of Howl et al. relies solely on the square of the atom number for sensitivity, yielding a weak signal; the recently proposed squeezing-enhanced dual-platform scheme by Li [2] amplifies the signal to but suffers from system complexity and cross-correlation difficulties. This paper simultaneously proposes two complementary experimental frameworks: Scheme A (Theoretical Benchmark) establishes a “gold standard” paradigm for quantum gravity tests within a rigorous theoretical framework (number-squeezing, precise Feshbach cancellation, exponential scaling law); Scheme B (Exploratory Precursor) is based on a set of engineering-friendly alternative assumptions (bidirectional quantum interface, gradient field spatial averaging, differential measurement), aiming for a near-term proof-of-principle exploration of the core phenomenon of “squeezing-enhanced non-Gaussian signals.” The two schemes share the same physical core: squeezing-enhanced non-Gaussian signals serve as a potential discriminative signature of quantum gravity. This paper details the theoretical foundations, experimental designs, feasibility assessments, and application scenarios of both schemes, providing alternative pathways for research groups with different experimental capabilities. Scheme B significantly lowers the environmental and technical barriers, making it possible to conduct proof-of-principle experiments in standard cold-atom laboratories; Scheme A provides a complete theoretical framework for future high-precision verification. The two schemes are proposed in parallel and complement each other, jointly forming a complete research roadmap from “preliminary detection” to “rigorous testing.” Keywords: quantum gravity; non-Gaussianity; BEC; squeezed states; tabletop experiments; theoretical benchmark; exploratory precursor 摘要 量子引力的实验检验长期受限于普朗克能标的极端能量尺度。近年来,利用桌面量子系统检验引力非高斯性的理论方案取得了重要进展,但现有方案在实验可行性上面临严峻挑战:Howl等人的BEC+Feshbach方案灵敏度仅依赖原子数平方 ,信号微弱;李政达 [2]