Fragmented Many-Body states of definite angular momentum and stability of attractive 3D Condensates

A three dimensional attractive Bose-Einstein Condensate (BEC) is expected to collapse, when the number of the particles $N$ in the ground state or the interaction strength $\lambda_0$ exceeds a critical value. We study systems of different particle numbers and interaction strength and find that even if the overall ground state is collapsed there is a plethora of fragmented excited states that are still in the metastable region. Utilizing the \emph{configuration interaction} expansion we determine the spectrum of the ground (`yrast') and excited many-body states with definite total angular momentum quantum numbers $0\leqslant L\leqslant N$ and $-L\leqslant M_L\leqslant L$, and we find and examine states that survive the collapse. This opens up the possibility of realizing a metastable system with overcritical numbers of bosons in a ground state with angular momentum $L\neq0$. The multi-orbital mean-field theory predictions about the existence of fragmented metastable states with overcritical numbers of bosons are verified and elucidated at the many-body level. The descriptions of the total angular momentum within the mean-field and the many-body approaches are compared.