Universal properties of a trapped two-component Fermi gas at unitarity

TL;DR

This paper investigates the universal properties of a trapped two-component Fermi gas at unitarity, revealing unique excitation features, confirming analytical wavefunction predictions, and determining the excitation gap up to 30 particles, aligning with density functional theory.

Contribution

The study provides the first accurate solutions for small systems and extends findings to larger systems, establishing universal excitation properties and the excitation gap in a trapped Fermi gas at unitarity.

Findings

No many-body bound states other than trap-bound ones.

Certain excitation frequencies are separated by 2ħω.

The excitation gap matches density functional predictions.

Abstract

We treat the trapped two-component Fermi system, in which unlike fermions interact through a two-body short-range potential having no bound state but an infinite scattering length. By accurately solving the Schroedinger equation for up to N=6 fermions, we show that no many-body bound states exist other than those bound by the trapping potential, and we demonstrate unique universal properties of the system: Certain excitation frequencies are separated by $2\hbar\omega$, the wavefunctions agree with analytical predictions and a virial theorem is fulfilled. Further calculations up to N=30 determine the excitation gap, an experimentally accessible universal quantity, and it agrees with recent predictions based on a density functional approach.