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

Abstract 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 近期提出的压缩增强双平台方案虽将信号放大至 ,但系统复杂、互相关困难。本文同时提出两种互补的实验框架:A方案(理论基准型) 在严格的理论框架内(数模压缩、Feshbach精确调零、指数标度律判决)建立量子引力检验的“黄金标准”范式;B方案(先导探索型) 基于一组可工程化的替代性假设(双向量子接口、梯度空间平均、差分测量),旨在近期内对“压缩增强的非高斯信号”这一核心现象进行原理性探索。两种方案共享同一物理内核:压缩增强的非高斯信号是量子引力的潜在判决性特征。本文详细阐述两种方案的理论基础、实验设计、可行性评估和适用场景,为不同实验条件的团队提供可选择的路径。B方案显著降低了实验的环境和技术门槛,使其可能在常规冷原子实验室内进行原理探索;A方案则为未来精密验证提供了完整的理论框架。两种方案并行提出,互为补充,共同构成从“初步探测”到“严格检验”的完整研究路线。 关键词:量子引力;非高斯性;BEC;压缩态;桌面实验;理论基准;先导探索