标题： 复合玻色子叠加 ansatz 方法研究一维囚禁少费米子系统 显示英文标题

标题： Composite Bosons Superposition Ansatz Approach to One-Dimensional Trapped Few-Fermion Systems

摘要： 超冷原子系统为探索量子现象提供了一个多功能平台，提供了可调的相互作用和多样的囚禁几何结构。 在这项研究中，我们使用复合玻色子形式主义来研究被囚禁的费米子的一维系统，该形式主义将自旋相反的费米子对描述为复合玻色子（简称coboson）。 通过构建coboson态的叠加假设，我们在吸引和排斥相互作用下求解了两个费米子对的薛定谔方程。 我们确定了关键可观测量，例如粒子密度分布和双体关联。 此外，我们计算了低能谱并估计了配对间隙。 我们的结果突显了coboson形式主义在探索强相关少体系统中的量子现象的潜力，并取得了与标准精确对角化技术相当的结果。 显示英文摘要

摘要： Ultra-cold atomic systems provide a versatile platform for exploring quantum phenomena, offering tunable interactions and diverse trapping geometries. In this study, we investigate a one-dimensional system of trapped fermionic atoms using the composite boson formalism, which describes pairs of opposite-spin fermions as cobosons (short for composite bosons). By constructing a superposition ansatz of coboson states, we solve the Schr\"odinger equation for two fermion pairs under both attractive and repulsive interactions. We determine key observables such as particle density profiles and two-body correlations. Additionally, we compute the low-lying energy spectrum and estimate the pairing gap. Our results highlight the potential of the coboson formalism for exploring quantum phenomena in strongly correlated few-body systems, achieving results comparable to standard exact diagonalization techniques.