Normal state of highly polarized Fermi gases: simple many-body approaches

TL;DR

This paper investigates the properties of a single impurity atom in a polarized Fermi gas near a Feshbach resonance, showing that simple many-body approaches can accurately describe the system's behavior even at unitarity.

Contribution

The study demonstrates that simple variational and T-matrix methods yield consistent results for impurity properties, aligning well with quantum Monte-Carlo and exact solutions, even at strong interactions.

Findings

Interaction effects are weaker than expected at unitarity.

Single particle-hole excitations suffice to describe the system.

Results agree with quantum Monte-Carlo and exact solutions.

Abstract

We consider the problem of a single \down atom in the presence of a Fermi sea of \up atoms, in the vicinity of a Feshbach resonance. We calculate the chemical potential and the effective mass of the \down atom using two simple approaches: a many-body variational wave function and a T-matrix approximation. These two methods lead to the same results and are in good agreement with existing quantum Monte-Carlo calculations performed at unitarity and, in one dimension, with the known exact solution. Surprisingly, our results suggest that, even at unitarity, the effect of interactions is fairly weak and can be accurately described using single particle-hole excitations. We also consider the case of unequal masses.