Spin-polarized Fermi superfluids as Bose-Fermi mixtures

TL;DR

This paper demonstrates that in the strong-coupling BEC regime, a spin-polarized Fermi superfluid can be effectively described as a Bose-Fermi mixture, with detailed analysis of interactions mediated by unpaired fermions.

Contribution

It derives an effective Bose-Fermi mixture description for a spin-polarized Fermi superfluid, including a beyond-Born approximation for dimer-fermion interactions at finite temperatures.

Findings

Reduction of Fermi superfluid to Bose-Fermi mixture in strong coupling

Derivation of effective dimer-fermion interaction beyond Born approximation

Calculation of s-wave scattering length $a_{BF}=1.18a_F$

Abstract

In the strong-coupling BEC region where a Feshbach resonance gives rise to tightly-bound dimer molecules, we show that a spin-polarized Fermi superfluid reduces to a simple Bose-Fermi mixture of Bose-condensed dimers and the leftover unpaired fermions. Using a many-body functional integral formalism, the Gaussian fluctuations give rise to an induced dimer-dimer interaction mediated by the unpaired fermions, with the dimer-fermion vertex being given by the (mean-field) Born approximation. Treating the pairing fluctuations to quartic order, we show how the action for a spin-polarized Fermi superfluid reduces to one for a Bose-Fermi mixture. This Bose-Fermi action includes an expression for the effective dimer-unpaired fermion interaction in a spin-polarized Fermi superfluid beyond the Born approximation, in the superfluid phase at finite temperatures. In the low-density limit, we show how this dimer-fermion interaction gives the s-wave scattering length $a_{BF}=1.18a_F$ ($a_F$ is the s-wave fermion scattering length), a result first derived by Skorniakov and Ter-Martirosian in 1957 for three interacting fermions.