# Few vs many-body physics of an impurity immersed in a superfluid of spin 1/2 attractive fermions

## TL;DR

This paper explores the behavior of an impurity in a superfluid of strongly correlated spin 1/2 fermions, analyzing stability, three-body interactions, and energy corrections beyond mean-field approximations.

## Contribution

It relates the stability of dimer and trimer states to the three-body problem and highlights the divergence of beyond-mean-field energy corrections requiring regularization.

## Key findings

- Stability diagram of dimer and trimer states linked to three-body physics.
- Beyond-mean-field energy corrections are divergent and need regularization.
- Proper accounting of three-body physics is essential for accurate impurity energy calculations.

## Abstract

In this article we investigate the properties of an impurity immersed in a superfluid of strongly correlated spin 1/2 fermions. For resonant interactions, we first relate the stability diagram of dimer and trimer states to the three-body problem for an impurity interacting with a pair of fermions. Then we calculate the beyond-mean-field corrections to the energy of a weakly interacting impurity. We show that these corrections are divergent and have to be regularized by properly accounting for three-body physics in the problem.