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 Schrödinger 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.

13 pages, 6 figures

References in corpus (21)

• Many-Body Physics with Ultracold Gases
• Observation of Bose-Einstein Condensation of Molecules
• Two Fermions in a double well: Exploring a fundamental building block of the Hubbard model
• Full configuration interaction approach to the few-electron problem in artificial atoms
• Observation of pair condensation in the quasi-2D BEC-BCS crossover
• Analytical solutions for the dynamics of two trapped interacting ultracold atoms
• Exact quantum Monte Carlo study of one dimensional trapped fermions with attractive contact interactions
• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Pairing of few Fermi atoms in one dimension
• Strongly interacting trapped one-dimensional quantum gases: an exact solution
• Evolution from few- to many-body physics in one-dimensional Fermi systems: One- and two-body density matrices, and particle-partition entanglement
• Two interacting fermions in a 1D harmonic trap: matching the Bethe ansatz and variational approaches
• Emergent interaction-driven elliptic flow of few fermionic atoms
• Magnetic impurity in a one-dimensional few-fermion system
• 2kF-Friedel to 4kF-Wigner oscillations in one-dimensional Fermi gases under confinement
• Composite-boson approach to molecular Bose-Einstein condensates in mixtures of ultracold Fermi gases
• A modular implementation of an effective interaction approach for harmonically trapped fermions in 1D
• Separable approximation to two-body matrix elements
• Correlated Pair Approach to Composite Boson Scattering Lengths
• Unconventional pairing in few-fermion systems at finite temperature
• Pairing correlations in a trapped one-dimensional Fermi gas