Eigenvalues of the one-body density matrix for correlated condensates Original Research Article

The competition between correlations and condensate formation is discussed qualitatively. The eigenvalues of the one-body density matrix provide a quantitative measure of the condensate fraction. We use symmetrized wave functions consisting of two Gaussians each depending on hyperradius and distance between pairs of particles. The eigenvalues are computed as functions of particle number N for attractive and repulsive two-body interactions. Center-of-mass and two-body correlations are computed. For repulsion the condensate fraction approaches unity with increasing N. It is large for small and moderate correlations, and decreases steeply when the correlations exceed a critical value.