Mass-gap description of heavy impurities in Fermi gases

TL;DR

This paper introduces a unified theoretical framework linking Fermi polarons and the Anderson orthogonality catastrophe, revealing a mass gap that influences impurity behavior and polaron-molecule transitions in Fermi gases.

Contribution

It develops a mean-field theory showing how a recoil-induced mass gap affects impurity states, connecting quasiparticle properties to many-body phenomena.

Findings

Identification of a mass gap as the origin of quasiparticle weight.

Derivation of a power-law scaling of quasiparticle weight with impurity mass ratio.

Explanation of the polaron-to-molecule transition through the in-gap state.

Abstract

We present a unified theory that connects the quasiparticle picture of Fermi polarons for mobile impurities to the Anderson orthogonality catastrophe for static impurities. By operator reordering of the underlying many-body Hamiltonian, we obtain a modified fermionic dispersion relation that features a recoil-induced energy gap, which we call the `mass gap'. We show that the resulting mean-field Hamiltonian exhibits an in-gap state for finite impurity mass, which takes a key role in Fermi polaron and molecule formation. We identify the mass gap as the microscopic origin of the quasiparticle weight of Fermi polarons and derive a power-law scaling of the weight with the impurity-to-fermion mass ratio. The associated in-gap state is shown to give rise to the emergence of the polaron-to-molecule transition away from the limiting case of the Anderson orthogonality catastrophe in which the transition is absent.