Effective interaction between molecules in the BEC regime of a superfluid Fermi gas

TL;DR

This paper analyzes the effective interaction between molecules in a superfluid Fermi gas's BEC regime, revealing the importance of a physical cutoff energy and showing how the molecular scattering length varies with temperature.

Contribution

It introduces a renormalization group analysis with a physical cutoff to clarify molecular interactions and scattering lengths in the BEC regime of superfluid Fermi gases.

Findings

The molecular scattering length is renormalized to include high-energy effects.

The scattering length depends strongly on temperature and vanishes at the critical temperature.

A physical cutoff energy from molecular binding energy is crucial for understanding interactions.

Abstract

We investigate the effective interaction between Cooper-pair molecules in the st rong-coupling BEC regime of a superfluid Fermi gas with a Feshbach resonance. Our work uses a path integral formulation and a renormalization group (RG) analy sis of fluctuations in a single-channel model. We show that a physical cutoff en ergy $\omega_c$ originating from the finite molecular binding energy is the key to understanding the interaction between molecules in the BEC regime. Our work t hus clarifies recent results by showing that $a_{\rm M}=2a_{\rm F}$ is a {\it ba re} molecular scattering length while $a_{\rm M}=(0.6\sim0.75) a_{\rm F}$ is the low energy molecular scattering length renormalized to include high-energy scat tering up to $\omega_c$ (here $a_{\rm F}$ is the scattering length between Fermi atoms). We also include many-body effects at finite temperatures. We find that $a_{\rm M}$ is strongly dependent on temperature, vanishing at $T_{\rm c}$, consistent with the earlier Bose gas results of Bijlsma and Stoof.