A smooth polaron-molecule crossover in a Fermi system

TL;DR

This paper investigates the transition of a single impurity in a Fermi sea from polaronic to molecular behavior, demonstrating that this crossover is smooth rather than abrupt, with implications for cold atom systems.

Contribution

It provides evidence that the polaron-molecule transition in a Fermi system is a smooth crossover, challenging previous claims of a sharp phase transition.

Findings

The crossover from polaron to molecule is smooth, not sharp.

The study compares Hubbard and gas models.

Implications for cold atom experiments.

Abstract

The problem of a single down spin particle interacting with a Fermi sea of up spin particles is of current interest in the field of cold atoms. The Hubbard model, appropriate to atoms in an optical lattice potential, is considered in parallel with a gas model. As the strength of an attractive short-range interaction is increased there is a crossover from "polaron" behaviour, in which the Fermi sea is weakly perturbed, to "molecule" behaviour in which the down spin particle is bound to a single up spin particle. It is shown that this is a smooth crossover, not a sharp transition as claimed by many authors.