Analytical theory of the dressed bound state in highly polarized Fermi gases

TL;DR

This paper develops an analytical diagrammatic approach to study a single impurity atom in a highly polarized Fermi gas, accurately describing the dressed bound state and aligning well with Monte Carlo results.

Contribution

It introduces a new analytical method using limited particle-hole excitations to analyze dressed bound states in polarized Fermi gases, extending to mass-imbalanced cases.

Findings

Excellent agreement with Monte Carlo simulations.

Reduces to Skorniakov and Ter-Martirosian equation in BEC limit.

Provides results for different mass ratios.

Abstract

We present an analytical treatment of a single \down atom within a Fermi sea of \up atoms, when the interaction is strong enough to produce a bound state, dressed by the Fermi sea. Our method makes use of a diagrammatic analysis, with the involved diagrams taking only into account at most two particle-hole pairs excitations. The agreement with existing Monte-Carlo results is excellent. In the BEC limit our equation reduces exactly to the Skorniakov and Ter-Martirosian equation. We present results when \up and \down atoms have different masses, which is of interest for experiments in progress.