Effects of quantum fluctuations on the dynamics of dipolar Bose polarons

We study the dynamics of dipolar Bose polarons in the presence of normal and anomalous fluctuations using the time-dependent Hartree-Fock-Bogoliubov theory. The density profiles of the condensate, the anomalous component and the impurity are deeply analyzed. The time evolution of the width and the center-of-mass oscillation of such quantities are also highlighted. We calculate corrections due to quantum fluctuations and impurity to the chemical potential and the radius of the condensate, and of the anomalous component, in the weak coupling regime using the Thomas-Fermi approximation. Effects of the dipole-dipole interaction, impurity-host interaction and the anomalous fluctuation on the width and on the breathing frequencies of the impurity are discussed by variational and numerical means.