Non-condensate fraction of a weakly interacting Bose gas confined between two parallel plates within improved Hartree-Fock approximation at zero temperature

By analytically solving the nonlinear gap and Schwinger-Dyson equations, the non-condensate fraction of a weakly interacting Bose-Einstein condensate (BEC) confined between two parallel plates at zero temperature is investigated within the improved Hartree-Fock approximation. It is proved that the finite-size effect increases the non-condensate fraction compared with the one of the same homogeneous BEC. Our result also shows that the non-condensate fraction can be expressed as a sum of two terms: the first term corresponds to the non-condensate fraction of the homogeneous dilute BEC and the other appears because of the confinement. Both terms are universal. A comparison with the experimental data is made. •Equation for condensate fraction of a dilute Bose gas is established in the improved Hartree-Fock approximation.•The effect caused by the confinement along z-direction on the condensate fraction is investigated at zero temperature.•The contribution of finite-size is proportional to ratio of scattering length to distance between two parallel plates.•Taking into account the influence of finite-size effect, the condensate fraction is still universal.•A comparison with experimental data is made.