Thermodynamics and Statistical Fluctuations for the Trapped Interacting Bose Gas

Abstract

We study the condensate fluctuation and several statistics of weakly interacting Bose gas by a correlated many-body approach -correlated potential harmonics method (CPHEM). We include all two-body correlations and realistic van der Waals interaction to probe real experimental situation which considers the mesoscopic condensate and go beyond the scope of mean-field and existing many-body theoretical methods like Diffusion Monte Carlo and Faddeev approach. We prescribe an ab initio but approximate many-body calculation which accurately calculates energy spectrum of the condensate. We consider attractive Bose gas of 7Li in harmonic trap and repulsive Bose gas of 87Rb both in harmonic and anharmonic trap. Experimental observation of atom number fluctuation for repulsive condensate of 87Rb by M. Kristensen et al. [144], increases the hope that in near future the same for attractive condensate will also be performed. We theoretically study the fluctuations properties like condensate fraction, root-mean-square fluctuation and different orders of central-moments of the condensates for both repulsive and attractive condensate. We observe the lambda-structure in all the fluctuation measures near the transition temperature which remain same qualitatively in all types of traps. We define three characteristic temperatures calculated from the point of inflexion of the lambda-structure which jointly confirm that the achievement of condensation is more favourable in anharmonic trap. The possibility of true phase transition is ruled out for all traps for the mesoscopic Bose Einstein condensation. The effect of interaction (repulsive and attractive) on the energy fluctuations of BEC in the mesoscopic regime is thoroughly studied and observed the effect of interatomic correlation for the attractive condensate. The possibility of phase transition is ruled out in the mesoscopic regime irrespective of the type of interactions.