Fermionic ground state at unitarity and Haldane Exclusion Statistics

TL;DR

This paper investigates the properties of a few-fermion system at unitarity, employing a generalized ETF method assuming Haldane-Wu FES, and finds results consistent with Monte Carlo calculations, offering a novel semiclassical approach.

Contribution

It introduces a generalized ETF approach assuming Haldane-Wu FES at unitarity, differing from previous scaled ETF methods, and aligns well with Monte Carlo results.

Findings

Semiclassical FES results match Monte Carlo calculations.

Method provides a new semiclassical perspective on fermionic systems at unitarity.

Results are consistent with existing theoretical models.

Abstract

We consider a few-particle system of trapped neutral fermionic atoms at ultra-low temperatures, with the attractive interaction tuned to Feshbach resonance. We calculate the energies and the spatial densities of the few-body systems using a generalisation of the extended Thomas-Fermi (ETF) method, and assuming the particles obey the Haldane-Wu fractional exclusion statistics (FES) at unitarity. This method is different from the scaled ETF version given by Chang and Bertsch (Phys. Rev. A76,021603(R) (2007)). Our semiclassical FES results are consistent with the Monte-Carlo calculations of the above authors, but can hardly be distinguished from their over all scaling of the ETF result at unitarity.