Cold atoms at unitarity and inverse square interaction

TL;DR

This paper explores the connection between the quantum spectrum of two atoms at unitarity and the inverse square potential, revealing a link to fractional exclusion statistics that aligns with experimental data.

Contribution

It demonstrates that the spectrum of two atoms at unitarity matches that of the inverse square potential, connecting it to fractional exclusion statistics and experimental results.

Findings

Spectrum matches inverse square potential

FES provides accurate description of Fermi gas at unitarity

Analytical virial coefficient supports FES application

Abstract

Consider two identical atoms in a spherical harmonic oscillator interacting with a zero-range interaction which is tuned to produce an s-wave zero-energy bound state. The quantum spectrum of the system is known to be exactly solvable. We note that the same partial wave quantum spectrum is obtained by the one-dimensional scale-invariant inverse square potential. Long known as the Calogero-Sutherland-Moser (CSM) model, it leads to Fractional Exclusion Statistics (FES) of Haldane and Wu. The statistical parameter is deduced from the analytically calculated second virial coefficient. When FES is applied to a Fermi gas at unitarity, it gives good agreement with experimental data without the use of any free parameter.