Polaron Properties of an Impurity in Bose-Einstein-Condensation

TL;DR

This paper investigates the properties of an impurity in a Bose-Einstein condensate at zero temperature, deriving a polaron model and calculating key impurity characteristics using Bogoliubov and LLP theories.

Contribution

It introduces a simplified Hamiltonian analogous to the Fröhlich Hamiltonian for large polarons and applies LLP theory to analyze impurity effective mass and energy.

Findings

Derived a reduced Hamiltonian similar to the Fröhlich Hamiltonian.

Calculated impurity effective mass and phonon number.

Discussed the validity range of the forward-scattering approximation.

Abstract

In this paper we study an impurity in Bose-Einstein-Condensate system at $T=0K$ and suppose the contact forms for boson-boson and boson-impurity interactions. Using Bogoliubov theory and a further approximation corresponding to only think over the forward scattering of impurity by bosons, we derive a reduced Hamiltonian whose form is the same as the Fr\"{o}hlich Hamiltonian for large polaron. By using Lee-Low-Pines (LLP) theory for large polaron, we obtain the effective mass of impurity, the phonon number carried by impurity and the energy related to the existence of impurity. In addition, we also discuss the valid range for forward-scattering approximation.