Generalized Hartree-Fock-Bogoliubov Description of the Frohlich Polaron

TL;DR

This paper develops a generalized Hartree-Fock-Bogoliubov approach to analyze Frohlich polarons in cold atom systems, revealing how unique phonon interactions influence polaron properties with results aligning closely with Feynman's method.

Contribution

It introduces a novel HFB-based framework for Frohlich polarons, especially Bose polarons in quasi-1D systems, incorporating artificial phonon interactions from the LLP transformation.

Findings

HFB method yields polaron energies close to Feynman's predictions.

Unique phonon-phonon interactions significantly affect polaron states.

Quasi-1D model avoids ultraviolet divergence, enabling accurate analysis.

Abstract

We adapt the generalized Hartree-Fock-Bogoliubov (HFB) method to an interacting many-phonon system free of impurities. The many-phonon system is obtained from applying the Lee-Low-Pine (LLP) transformation to the Frohlich model which describes a mobile impurity coupled to noninteracting phonons. We specialize our general HFB description of the Frohlich polaron to Bose polarons in quasi-1D cold atom mixtures. The LLP transformed many-phonon system distinguishes itself with an artificial phonon-phonon interaction which is very different from the usual two-body interaction. We use the quasi-one-dimensional model, which is free of an ultraviolet divergence that exists in higher dimensions, to better understand how this unique interaction affects polaron states and how the density and pair correlations inherent to the HFB method conspire to create a polaron ground state with an energy in good agreement with and far closer to the prediction from Feynman's variational path integral approach than mean-field theory where HFB correlations are absent.