The macroscopic occupation of atoms in the ground state of an interacting Bose gas confined by an external harmonic potential is calculated as a function of the interaction strength. The effect of the inter-atomic interaction to the ground state distribution is discussed.
Interacting Bose gas confined by an external potential is studied using Green functions in spectral representation. The calculation is presented transparently using the equation of motion method. With this, the interplay between the condensed and the non-condensed atoms is inevitably seen. An expression for the condensate number at finite temperature is obtained in the lowest and first orders, from which depletion of bosons from the ground state is qualitatively analyzed. Finally, we discuss the behaviour of the specific heat of a trapped interacting Bose gas in the quasi-continuum limit.
We determine the exact many-body properties of a bosonic Tonks-Girardeau gas confined in a harmonic potential with a tunable $\ensuremath{\delta}$-function barrier at the trap center. This is done by calculating the reduced single-particle density matrix, the pair-distribution function, and the momentum distribution of the gas as a function of barrier strength and particle number. With increasing barrier height we find that the ground-state occupation in a diagonal basis diverges from the N behavior that is expected for the case of a simple harmonic trap. In fact, the scaling of the occupation number depends on whether one has an even or odd number of particles. Since this quantity is a measure of the coherence of our sample we show how the odd-even effect manifests itself in both the momentum distribution of the Bose gas and interference fringe visibility during free temporal evolution.