We suggest a practical way to estimate the condensate fraction of an interacting dilute Bose gas confined by an external harmonic potential as a function of temperature and scattering length. It shows that an increase of the scattering length produces an exponential decrease of condensate fraction.
The ground state of a gas of Bosons confined in an external trap potential and interacting via repulsive two-body forces has recently been shown to exhibit complete Bose-Einstein condensation in the dilute limit, yielding for the first time a rigorous proof of this phenomenon in a physically realistic setting. We give here an account of this work about the Gross-Pitaevskii limit where the particle number N goes to infinity with Na fixed, where a is the scattering length of the interparticle interaction, measured in units of the trap size.
Present experiments with Bose condensed gases can be largely described by a semi-ideal two-gas model. In this model, the condensate is influenced only by the mean-field repulsion among condensed atoms, while the thermal cloud is considered an ideal gas confined by an effective potential that consists of the external trap and the mean-field repulsion by the condensate. This simple, intuitive model provides explicit analytical expressions for the density distributions of the condensate and the thermal component. It describes the reduction of the condensate fraction relative to that of an ideal gas as a consequence of the positive chemical potential due to interactions in the condensate.
The critical temperature and condensate fraction of a trapped interacting Bose gas are investigated when both atom-atom interaction and finite-size effects are taken into account. A canonical ensemble is used to obtain the equations on the condensate fraction for the trapped interacting Bose gas near and below the critical temperature. In our approaches corrections due to atom-atom interaction and finite-size effects are obtained simultaneously for the critical temperature and condensate fraction of the system. An analytical high-order correction to the condensate fraction is given.
By using a mean-field approach, based on the Popov approximation, we calculate the temperature dependence of the condensate fraction of an interacting Bose gas of N atoms confined in an anisotropic harmonic trap. For systems interacting with repulsive forces we find a significant decrease of the condensate fraction and of the critical temperature with respect to the predictions of the noninteracting model with the same value of N. An analytic result for the shift of the critical temperature holding to first order in the scattering length is also derived. \textcopyright{} 1996 The American Physical Society.