Feynman path-integral treatment of the BEC-impurity polaron

TL;DR

This paper applies Feynman's path-integral method to analyze Bose-Einstein condensate impurity polarons, deriving a coupling strength expression and exploring the transition between free and self-trapped polarons.

Contribution

It introduces a Feynman path-integral approach to calculate polaron properties across all coupling strengths in BECs, linking theory to experimental parameters.

Findings

Derived a polaronic coupling strength relating to experimental parameters.

Calculated free energy and effective mass shifts for all coupling strengths.

Indications of a transition from free to self-trapped polarons.

Abstract

The description of an impurity atom in a Bose-Einstein condensate can be cast in the form of Frohlich's polaron Hamiltonian, where the Bogoliubov excitations play the role of the phonons. An expression for the corresponding polaronic coupling strength is derived, relating the coupling strength to the scattering lengths, the trap size and the number of Bose condensed atoms. This allows to identify several approaches to reach the strong-coupling limit for the quantum gas polarons, whereas this limit was hitherto experimentally inaccessible in solids. We apply Feynman's path-integral method to calculate for all coupling strengths the polaronic shift in the free energy and the increase in the effective mass. The effect of temperature on these quantities is included in the description. We find similarities to the acoustic polaron results and indications of a transition between free polarons and self-trapped polarons. The prospects, based on the current theory, of investigating the polaron physics with ultracold gases are discussed for lithium atoms in a sodium condensate.