Generalized Hartree-Fock-Bogoliubov Description of the Frohlich Polaron

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.

14 pages, 4 figures

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Cited by in corpus (4)

• Impurity states in the one-dimensional Bose gas
• Hartree-Fock treatment of Fermi polarons using the Lee-Low-Pine transformation
• Breathing modes of repulsive polarons in Bose-Bose mixtures
• Pulse and continuously driven many-body quantum dynamics of bosonic impurities in a Bose-Einstein condensate