Ground state of a tightly bound composite dimer immersed in a Fermi Sea

TL;DR

This paper presents a theoretical analysis of the ground state of a tightly bound impurity dimer in a Fermi sea, revealing the effects of its composite nature through systematic expansion and variational methods.

Contribution

It introduces a two-channel formalism to systematically expand the ground state energy of an impurity dimer in a Fermi sea up to third order in scattering length, highlighting the dimer's composite features.

Findings

First signature of the dimer's composite nature at order a^3

Accurate dimer energy estimates at large scattering length

Systematic expansion up to two particle-hole pairs

Abstract

In this paper we present a theoretical investigation for the ground state of an impurity immersed in a Fermi sea. The molecular regime is considered where a two-body bound state between the impurity and one of the fermions is formed. Both interaction and exchange of the bound fermion take place between the dimer and the Fermi sea. We develop a formalism based on a two channel model allowing us to expand systematically the ground state energy of this immersed dimer with the scattering length $a$. Working up to order $a^3$, associated to the creation of two particle-hole pairs, reveals the first signature of the composite nature of the bosonic dimer. Finally, a complementary variational study provides an accurate estimate of the dimer energy even at large scattering length.