Fermionic ground state at unitarity and Haldane exclusion statistics

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 generalization 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. Our semiclassical FES results are consistent with the Monte Carlo calculations of the above authors, but can hardly be distinguished from their overall scaling of the ETF result at unitarity.