  Motivated by the recent experiment [R. Lopes et. al., Phys. Rev. Lett. 119,
190404 (2017)] with a homogeneous Bose gas, we investigate a homogeneous dilute
Bose gas to calculate the quantum depletion density. By means of the
Cornwall-Jackiw-Tomboulis effective action approach within an improved
Hartree-Fock approximation, the condensed fraction is recovered in a simpler
manner and compared with corresponding findings in experimental data.
Additionally, higher-order terms are taken into account for several physical
quantities, in particular for the chemical potential and free energy density.
