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

The condensed fraction of a homogeneous dilute Bose gas within the improved Hartree-Fock approximation