Effective mass and interaction energy of heavy Bose polarons at unitarity

TL;DR

This paper investigates the properties of heavy Bose polarons at unitarity, deriving their effective mass and interaction energy using a perturbative approach to the Gross-Pitaevskii equation, applicable across different coupling regimes.

Contribution

It introduces a perturbative method to analyze heavy Bose polarons at unitarity, providing explicit calculations of effective mass and interaction energy.

Findings

Calculated the effective mass of heavy Bose polarons at unitarity.

Determined the interaction energy between two distant polarons at unitarity.

Reproduced known results in the weak coupling limit.

Abstract

We study the motion of a heavy impurity immersed in a weakly interacting BEC using the Gross-Pitaevskii equation (GPe). We construct a perturbative solution to the GPe in powers of impurity velocity in the case when the boson-impurity potential is tuned to unitarity and calculate the effective mass of the polaron. In addition, we calculate the interaction energy of two unitary polarons which are sufficiently far apart. Our formalism also reproduces the results for both the mass and interaction energy obtained at weak boson-impurity coupling.