Feynman path-integral treatment of the Bose polaron beyond the Fröhlich model

Abstract

An impurity immersed in a Bose-Einstein condensate is no longer accurately described by the Fröhlich Hamiltonian as the coupling between the impurity and the boson bath gets stronger. We study the dominant effects of the twophonon terms beyond the Fröhlich model on the ground state properties of the polaron using Feynman's variational path-integral approach. The previously reported discrepancy in the effective mass between the renormalization group approach and this theory is shown to be absent in the beyond-Fröhlich model on the positive side of the Feshbach resonance. Self-trapping, characterized by a sharp and dramatic increase of the effective mass, is no longer observed for the repulsive polaron once the two-phonon interactions are included. For the attractive polaron we find a divergence of the ground state energy and effective mass at weaker couplings than previously observed within the Fröhlich model. * timour.ichmoukhamedov@uantwerpen.be arXiv:1905.07368v1 [cond-mat.quant-gas]

Strong-coupling Bose polarons in one dimension: Condensate deformation and modified Bogoliubov phonons

“…The resulting (extended) Fröhlich Hamiltonian is formally identical to the one used in solid-state systems [25], amended with two-phonon scattering terms. Efficient approaches for its solution beyond the perturbative regime have been developed in the past, including variational [24,26,27], field-theoretical [19,[28][29][30], renormalization group (RG) [23,31], and opensystem approaches [32], as well as quantum Monte-Carlo simulations [23,33,34]. However, as well known from the example of electrons in superfluid helium, a strongly interacting impurity can also distort the superfluid itself [35].…”

Microscopic Derivation of the Fröhlich Hamiltonian for the Bose Polaron in the Mean-Field Limit

“…One of elements of our analysis below is the justification of this additional step while checking that the other steps, known to be rigorously justifiable in the meanfield case in the absence of an impurity, are still applicable. It is important, however, to realize that in some instances, especially when the impurity-boson interaction is strong, additional terms not present in the Fröhlich Hamiltonian (1.10) cannot be neglected [19][20][21].…”

Many-body quantum dynamics and induced correlations of Bose polarons

“…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].…”