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

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 $a_{\mathrm{M}}=2a_{\mathrm{F}}$ is a {\it ba re} molecular scattering length while $a_{\mathrm{M}}=(0.6\sim 0.75)a_{\mathrm{F}}$ is the low energy molecular scattering length renormalized to include high-energy scat tering up to ${\omega }_c$ (here $a_{\mathrm{F}}$ is the scattering length between Fermi atoms). We also include many-body effects at finite temperatures. We find that $a_{\mathrm{M}}$ is strongly dependent on temperature, vanishing at $T_{\mathrm{c}}$, consistent with the earlier Bose gas results of Bijlsma and Stoof.

10 pages, 3 figures