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arXiv · 0809.1892

Universal Properties of the Ultra-Cold Fermi Gas

Shizhong Zhang·Anthony J. Leggett
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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.

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Shizhong Zhang, Anthony J. Leggett. 2008-09-10. Universal Properties of the Ultra-Cold Fermi Gas. https://doi.org/10.1103/physreva.79.023601

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