Renormalisation Flow and Universality for Ultracold Fermionic Atoms

TL;DR

This paper uses the functional renormalisation group to analyze the BEC-BCS crossover in ultracold fermionic gases, revealing universal behavior governed by a fixed point and quantifying the universality's accuracy for specific atomic gases.

Contribution

It identifies the fixed point responsible for universality in the BEC-BCS crossover and computes universal ratios and the scope of universality for Li and K gases.

Findings

Universal ratio between molecular and atomic scattering lengths computed.

Universality depends only on concentration a k_F and temperature in units of Fermi energy.

Estimate of universality accuracy for Li and K gases provided.

Abstract

A functional renormalisation group study for the BEC-BCS crossover for ultracold gases of fermionic atoms is presented. We discuss the fixed point which is at the origin of universality for broad Feshbach resonances. All macroscopic quantities depend only on one relevant parameter, the concentration a k_F, besides their dependence on the temperature in units of the Fermi energy. In particular, we compute the universal ratio between molecular and atomic scattering length in vacuum. We also present an estimate to which level of accuracy universality holds for gases of Li and K atoms.