Data set for "Bounds on the detection of Bell correlations with entangled ultracold atoms in optical lattices under occupation defects"

Bell nonlocality stems from quantum correlations effectively identified using inequalities. Spin chains, simulated with ultracold atoms in optical lattices, Rydberg atoms in tweezer arrays, trapped ions, or molecules allow single-spin control and measurement. Therefore, they are suitable for studying fundamental aspects of these correlations and nonlocality. Occupation defects, such as vacancies or multiple atoms occupying a single site due to imperfect system preparation, limit the detection of Bell correlations. We study their effects with the help of a simplified toy model parametrized by the probability 𝑝 of having a single occupation for a given site. Within this model, and for entangled systems obtained by one-axis twisting evolution from an initial factorized state, we derive two Bell inequalities, one based on many-site correlations and the other on two-site correlations, and identify the smallest probability 𝑝 that allows the Bell inequalities violation to be detected. We then consider two physical realizations using entangled ultracold atoms in optical lattices where the parameter 𝑝 is related to a nonunitary filling factor and nonzero temperature. We test the predictions of the toy model against exact numerical results.The zip file contains all figures in the pdf or png format. Details on the analytical derivation of the bounds for toy model. Numerical data.

贝尔非定域性（Bell nonlocality）源于可通过不等式有效识别的量子关联。自旋链（Spin chains）可通过光晶格中的超冷原子、光镊阵列中的里德堡原子、囚禁离子或分子进行模拟，允许单自旋控制与测量。因此，它们适用于研究这些关联及非定域性的基本方面。占据缺陷（Occupation defects）——例如因系统制备不完善导致的空位或多个原子占据单个格点——限制了贝尔关联的探测。我们借助一个简化的玩具模型（toy model）研究其影响，该模型由给定格点单个占据的概率𝑝参数化。在该模型中，对于通过单轴扭曲演化（one-axis twisting evolution）从初始因子化状态（initial factorized state）获得的纠缠系统，我们推导了两个贝尔不等式：一个基于多格点关联，另一个基于两格点关联，并确定了允许探测贝尔不等式违背（Bell inequalities violation）的最小单个占据概率𝑝。随后，我们考虑两种物理实现，即利用光晶格中的纠缠超冷原子，其中参数𝑝与非幺正填充因子及非零温度相关。我们将玩具模型的预测与精确数值结果进行对比验证。压缩包包含所有PDF或PNG格式的图表、玩具模型边界的解析推导细节以及数值数据。