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

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.