Generalized Hartree-Fock-Bogoliubov description of the Fröhlich 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 Fröhlich model which describes a mobile impurity coupled to noninteracting phonons. We specialize our general HFB description of the Fröhlich 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.

Many-body quantum dynamics and induced correlations of Bose polarons

“…13, and ω f ≈26.26 appear in A(ω f ) whilst for N I =2 and g II =0 five dominantly contributing frequencies located at ω f ≈22. 31, ω f ≈23. 81, ω f ≈25.2, ω f ≈26.…”

“…Experimentally Bose [20][21][22][23][24] and Fermi [12,13,17] polarons have been observed and these experiments confirmed the importance of higher-order correlations for the description of the polaronic properties. The experiments in turn have spurred additional several theoretical investigations which have aimed at describing different polaronic aspects [25,26] by operating e.g.within the Fröhlich model [27][28][29][30][31], effective Hamiltonian approximations [8,[32][33][34], variational approaches [7,9,22,[35][36][37], renormalization group methods [25,38,39] and the path integral formalism [40,41].…”

Bose polarons in ultracold atoms in one dimension: beyond the Fröhlich paradigm

“…Numerous theoretical works have addressed the problem of a mobile impurity in an ultracold quantum gas, see [10,11] for reviews. However, they were either based on an effective Fröhlich Hamiltonian to describe the polaron [5,[12][13][14][15][16][17][18][19] or used truncated wave functions with only a few excitations [20,21]. Notable exceptions include a third-order perturbative treatment of the problem [22], a self-consistent T-matrix calculation [23], a mean-field (MF) analysis beyond the Fröhlich Hamiltonian [24], diffusion Monte Carlo (DMC) calculations based on the full microscopic Hamiltonian [25,26] and approximate analytical descriptions [27,28].…”

Dissipative correlated dynamics of a moving impurity immersed in a Bose–Einstein condensate

“…These experiments triggered an intense theoretical activity in order to describe the polaron characteristics by operating within different frameworks [31,32]. These include, but are not restricted to, the mean-field approximation [33][34][35][36], the Fröhlich model [37][38][39][40][41][42], variational methods [14,17,24,25,27], effective Hamiltonian approaches [16,21,43,44] and renormalization group techniques [20,31,45]. While the majority of these investigations have been mainly focused on the equilibrium properties of the emergent quasiparticles, the dynamics of impurities is far less explored.…”