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

TL;DR

This paper provides exact solutions for three attractively interacting fermions in a harmonic trap, exploring ferromagnetism onset and high-temperature thermodynamics, offering benchmarks for experiments and simulations.

Contribution

It presents the first exact solutions for three fermions near a Feshbach resonance and analyzes their implications for ferromagnetism and thermodynamics.

Findings

Fully polarized fermions are stable against spin-flip at positive scattering length.

Calculated second and third virial coefficients for thermodynamics.

Equations of state serve as benchmarks for experiments and simulations.

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 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.