Three attractively interacting fermions in a harmonic trap: Exact solution, ferromagnetism, and high-temperature thermodynamics

Journal Article · Sun Aug 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.023619· OSTI ID:21448558

Xiaji, Liu; Hui, Hu; Drummond, Peter D ^[1]

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1. ARC Centre of Excellence for Quantum-Atom Optics, Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne 3122 (Australia)

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 s-wave scattering length a is sufficiently positive, three fully polarized fermions are energetically stable against a single spin-flip, indicating the possibility of itinerant ferromagnetism, as inferred in the recent experiment. We also investigate the high-temperature 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.

• OSTI ID: 21448558
• Journal Information: Physical Review. A, Vol. 82, Issue 2; Other Information: DOI: 10.1103/PhysRevA.82.023619; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

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