Cold atoms at unitarity and semiclassical ground state of a Fermi gas for Haldane-Wu exclusion statistics

TL;DR

This paper develops a semiclassical theory for cold atoms at unitarity using Haldane-Wu exclusion statistics, accurately predicting ground state energies and densities in harmonic traps, consistent with numerical simulations.

Contribution

It introduces a parameter-free semiclassical approach based on FES to model cold atomic systems at unitarity, aligning well with existing numerical results.

Findings

Accurate ground state energy predictions for trapped cold atoms.

Consistent particle density calculations with numerical simulations.

Validation of FES-based semiclassical theory against established data.

Abstract

We investigate finite particle systems of cold atoms bound in a local potential V(r). We derive the ground state energy and the particle density using a recently developed semiclassical theory (2008 Phys. Rev. Lett. 100 200408), and assuming the particles are described by the Haldane-Wu fractional exclusion statistics (FES) at unitarity. This approach is applied to atoms trapped into a three dimensional harmonic oscillator. We show that the parameter-free FES semiclassical theory yields results that are consistent with numerical simulations by Chang and Bertsch [2007 Phys. Rev A 76 021603(R)] and Bulgac (2007 Phys. Rev. A 76 040502).