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

Abstract: 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.