Polarons and dressed molecules near narrow Feshbach resonances

TL;DR

This paper investigates how narrow Feshbach resonances influence impurity quasiparticles in a Fermi sea, revealing analytic relations for ground state energy and dressing cloud size, extending understanding of impurity physics.

Contribution

It provides new analytic results on impurity quasiparticles near narrow Feshbach resonances, including a perturbative energy expression and a novel Tan's relation linking energy to dressing cloud size.

Findings

Ground state energy becomes perturbative in inverse range for large resonance range.

Derived a new Tan's relation connecting impurity energy to dressing cloud size.

At unitarity, the dressing cloud size is proportional to the negative of the ground state energy.

Abstract

The properties of impurities immersed in a large Fermi sea are naturally described in terms of dressed quasiparticles: attractive and repulsive polarons, and dressed molecules. Motivated by recent experiments on narrow Feshbach resonances, we analyze here how the quasiparticle properties are affected by a non-zero resonance range. We find two interesting analytic results. For large range, the ground state energy close to resonance is shown to become perturbative in the inverse range. In the limit of broad resonance instead, we provide a new Tan's relation linking the impurity ground state energy $E_\downarrow$ to the number of atoms in its dressing cloud $\Delta N$. As a corollary, at unitarity one finds $\Delta N=-E_\downarrow/\epsilon_F $, with $\epsilon_F$ the Fermi energy of the bath.