Universal Properties of the Ultra-Cold Fermi Gas

TL;DR

This paper explores the universal properties of a two-component ultra-cold Fermi gas across the BEC-BCS crossover, introducing a single function that encapsulates many-body physics and relates various physical quantities.

Contribution

It introduces a universal function $h(\xi,\tau)$ that describes the interaction and ground state energies, linking multiple physical properties in ultra-cold Fermi gases.

Findings

Interaction and ground state energies depend on a single universal function.

RF-spectroscopy shift and molecular fraction share the same temperature dependence.

Theoretical predictions are testable in future experiments.

Abstract

We present some general considerations on the properties of a two-component ultra-cold Fermi gas along the BEC-BCS crossover. It is shown that the interaction energy and the ground state energy can be written in terms of a single dimensionless function $h({\xi,\tau})$, where $\xi=-(k_Fa_s)^{-1}$ and $\tau=T/T_F$. The function $h(\xi,\tau)$ incorporates all the many-body physics and naturally occurs in other physical quantities as well. In particular, we show that the RF-spectroscopy shift $\bar{\d\o}(\xi,\tau)$ and the molecular fraction $f_c(\xi,\tau)$ in the closed channel can be expressed in terms of $h(\xi,\tau)$ and thus have identical temperature dependence. The conclusions should have testable consequences in future experiments.