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Spectral weight suppression in response functions of ultracold fermion-boson mixtures

We study the dynamical response of ultracold fermion-boson mixture in the Bogoliubov regime, where the interactions between fermionic impurities and bosonic excitations (phonons) are described by an effective Frohlich 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 diagrammatic technique we compute the Bragg spectra as well as the momentum dependent force-force correlation function. We fnd that both of them are heavily affected by the spectral weight suppression effect at low impurity densities in both 1D and 2D systems. We show that the the spectral weight suppression feature in Bragg spectra, which was previously found in the quantum Monte Carlo simulations and which cannot be recovered by the random phase approximation, can be accurately reproduced with the help of vertex corrections.