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Proceedings of the Physical Society

Fermion impurities in a weakly interacting Bose gas

Yvonne Lange

Published May 1, 1967• 0 citations
Publisher

Abstract

The Green function is derived for a small concentration of fermions in a weakly interacting Bose gas using mass operator perturbation theory. For small momentum it is found that the spectral weight function of the system consists of a quasi-particle peak associated with an effective mass m* as well as some weight at higher energies The momentum dependence of both parts of the spectral weight function is determined. The implications of the weight at higher energies in the case of dilute 3He-4He mixtures are discussed.

DOI
10.1088/0370-1328/91/1/326

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The Green function is derived for a small concentration of fermions in a weakly interacting Bose gas using mass operator perturbation theory. For small momentum it is found that the spectral weight function of the system consists of a quasi-particle peak associated with an effective mass m* as well as some weight at higher energies The momentum dependence of both parts of the spectral weight function is determined. The implications of the weight at higher energies in the case of dilute 3He-4He mixtures are discussed.
We study the dynamical response of ultracold fermion-boson mixtures in the Bogoliubov regime, where the interactions between fermionic impurities and bosonic excitations (phonons) are described by an effective Fr\"ohlich model under the Bogoliubov approximation. A characteristic suppression of the single-particle spectral weight is found in the small-momentum region where the impurity band and phonon mode intersect. Using a diagrammatic technique we compute the Bragg spectra as well as the momentum-dependent force-force correlation function. We find that both of them are heavily affected by the spectral weight suppression effect at low impurity densities in both one- and two-dimensional systems. We show that the spectral weight suppression feature in Bragg spectra, which was previously found in quantum Monte Carlo simulations and which cannot be recovered by the random phase approximation, can be accurately reproduced with the help of vertex corrections.
We investigate the properties of a dilute boson-fermion mixture at zero temperature. The ground-state energy of the system is calculated to second order in the Bose-Fermi coupling constant. The Green's function formalism is applied to obtain results for the effect of Bose-Fermi interactions on the spectrum of phonon excitations, the momentum distribution, the condensate fraction, and the superfluid density of the bosonic component. A quantitative discussion of these effects is presented in the case of mixtures with attractive interspecies interaction.
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We consider the movement of a 3He impurity atom in the Bose liquid. We suggest to describe the many-particle correlations between atoms of the Bose liquid, by using a deformed Heisenberg algebra. As generalized coordinates, we choose the collective variables that are the Fourier components of fluctuations of the density of Bose particles. The wave function of the investigated system in the zeroth approximation is the product of the wave function of the liquid helium-4 within deformed commutation relations between generalized coordinates and momenta and the plane wave of the impurity atom. We calculate the correction to the ground-state energy of the system “Bose liquid plus impurity” and the effective mass of the impurity atom 3He, by assuming that the boson-impurity interaction is a small perturbation.