Three attractively interacting fermions in a harmonic trap: Exact solution, ferromagnetism, and hightemperature thermodynamics
Abstract
Three fermions with strongly repulsive interactions in a spherical harmonic trap constitute the simplest nontrivial system that can exhibit the onset of itinerant ferromagnetism. Here, we present exact solutions for three trapped, attractively interacting fermions near a Feshbach resonance. We analyze energy levels on the upper branch of the resonance where the atomic interaction is effectively repulsive. When the swave scattering length a is sufficiently positive, three fully polarized fermions are energetically stable against a single spinflip, indicating the possibility of itinerant ferromagnetism, as inferred in the recent experiment. We also investigate the hightemperature thermodynamics of a strongly repulsive or attractive Fermi gas using a quantum virial expansion. The second and third virial coefficients are calculated. The resulting equations of state can be tested in future quantitative experimental measurements at high temperatures and can provide a useful benchmark for quantum Monte Carlo simulations.
 Authors:

 ARC Centre of Excellence for QuantumAtom Optics, Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne 3122 (Australia)
 Publication Date:
 OSTI Identifier:
 21448558
 Resource Type:
 Journal Article
 Journal Name:
 Physical Review. A
 Additional Journal Information:
 Journal Volume: 82; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.82.023619; (c) 2010 The American Physical Society; Journal ID: ISSN 10502947
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; BENCHMARKS; COMPUTERIZED SIMULATION; ENERGY LEVELS; EQUATIONS OF STATE; EXACT SOLUTIONS; EXPANSION; FERMI GAS; FERMIONS; FERROMAGNETISM; INTERATOMIC FORCES; MONTE CARLO METHOD; RESONANCE; S WAVES; SCATTERING LENGTHS; SPHERICAL CONFIGURATION; SPIN FLIP; THERMODYNAMICS; TRAPPING; TRAPS; CALCULATION METHODS; CONFIGURATION; DIMENSIONS; EQUATIONS; LENGTH; MAGNETISM; MATHEMATICAL SOLUTIONS; PARTIAL WAVES; SIMULATION
Citation Formats
Xiaji, Liu, Hui, Hu, and Drummond, Peter D. Three attractively interacting fermions in a harmonic trap: Exact solution, ferromagnetism, and hightemperature thermodynamics. United States: N. p., 2010.
Web. doi:10.1103/PHYSREVA.82.023619.
Xiaji, Liu, Hui, Hu, & Drummond, Peter D. Three attractively interacting fermions in a harmonic trap: Exact solution, ferromagnetism, and hightemperature thermodynamics. United States. https://doi.org/10.1103/PHYSREVA.82.023619
Xiaji, Liu, Hui, Hu, and Drummond, Peter D. Sun .
"Three attractively interacting fermions in a harmonic trap: Exact solution, ferromagnetism, and hightemperature thermodynamics". United States. https://doi.org/10.1103/PHYSREVA.82.023619.
@article{osti_21448558,
title = {Three attractively interacting fermions in a harmonic trap: Exact solution, ferromagnetism, and hightemperature thermodynamics},
author = {Xiaji, Liu and Hui, Hu and Drummond, Peter D},
abstractNote = {Three fermions with strongly repulsive interactions in a spherical harmonic trap constitute the simplest nontrivial system that can exhibit the onset of itinerant ferromagnetism. Here, we present exact solutions for three trapped, attractively interacting fermions near a Feshbach resonance. We analyze energy levels on the upper branch of the resonance where the atomic interaction is effectively repulsive. When the swave scattering length a is sufficiently positive, three fully polarized fermions are energetically stable against a single spinflip, indicating the possibility of itinerant ferromagnetism, as inferred in the recent experiment. We also investigate the hightemperature thermodynamics of a strongly repulsive or attractive Fermi gas using a quantum virial expansion. The second and third virial coefficients are calculated. The resulting equations of state can be tested in future quantitative experimental measurements at high temperatures and can provide a useful benchmark for quantum Monte Carlo simulations.},
doi = {10.1103/PHYSREVA.82.023619},
url = {https://www.osti.gov/biblio/21448558},
journal = {Physical Review. A},
issn = {10502947},
number = 2,
volume = 82,
place = {United States},
year = {2010},
month = {8}
}