Separable effective interaction for the trapped Fermi gas: The BEC-BCS crossover

2011/08/12 by C. N. Gilbreth, Y. Alhassid · 7 citations
Physics and Astronomy · #Atomic and Subatomic Physics Research #Cold Atom Physics and Bose-Einstein Condensates #Crossover #Eigenvalues and eigenvectors #Fermi Gamma-ray Space Telescope #Fermi gas #Interaction energy #Physics #Pseudopotential #Quantum electrodynamics #Quantum mechanics #Scattering #Scattering length #Strong Light-Matter Interactions #Unitarity #cond-mat.quant-gas #nucl-th #physics.atom-ph

paper · pdf · doi:10.1103/physreva.85.033621

published in Physical Review A 85(3) (American Physical Society) · 10 pages, 7 figures

arxiv created 2011/08/12 · openalex publication_date 2012/03/15 · arxiv updated 2012/06/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We extend a recently introduced separable interaction for the unitary trapped Fermi gas to all values of the scattering length. We derive closed expressions for the interaction matrix elements and the two-particle eigenvectors. At unitarity we analytically demonstrate the convergence of this interaction to the zero-range two-body pseudopotential for s-wave scattering. We apply this effective interaction to the three- and four-particle systems along the BEC-BCS crossover and find that their low-lying energies exhibit convergence in the regularization parameter that is much faster than for the conventional renormalized contact interaction. We find similar convergence properties of the three-particle free energy at unitarity.

Citations

• Many-body physics with ultracold gases
• Critical Temperature and Thermodynamics of Attractive Fermions at Unitarity
• Universal Properties of a Trapped Two-Component Fermi Gas at Unitarity
• Generalized virial theorem and pressure relation for a strongly correlated Fermi gas
• Energy spectrum of harmonically trapped two-component Fermi gases: Three- and four-particle problem
• Shell-model Monte Carlo simulations of the BCS-BEC crossover in few-fermion systems
• Universal properties of the ultracold Fermi gas
• Level crossing in the three-body problem for strongly interacting fermions in a harmonic trap
• New Effective Interaction for the Trapped Fermi Gas
• Thermodynamics of a Trapped Unitary Fermi Gas