  We investigate quantum gravity corrections due to the generalized uncertainty
principle on three-dimensional weakly interacting Bose gases at both zero and
finite temperatures using the time-dependent Hatree-Fock-Bogoliubov theory. We
derive useful formulas for the depletion, the anomalous density and some
thermodynamic quantities such as the chemical potential, the ground-state
energy, the free energy, and the superfluid density. It is found that the
presence of a minimal length leads to modify the fluctuations of the condensate
and its thermodynamic properties in the weak and strong quantum gravitational
regimes. Unexpectedly, the interplay of quantum gravity effects and quantum
fluctuations stemming from interactions may lift both the condensate and the
superfluid fractions. We show that quantum gravity minimizes the interaction
force between bosons leading to the formation of ultradilute Bose condensates.
Our results which can be readily probed in current experiments may offer a new
attractive possibility to understand gravity in the framework of quantum
mechanics.
