The impact of angular momentum on the stability and fragmentation of two- and three-dimensional attractive Bose-Einstein condensates

Abstract

In this Dissertation the physics of trapped, attractive Bose-Einstein condensates in two and three spatial dimensions are examined. Particular emphasis is put on the collapse of the gas, when the attractive interparticle interaction is raised above a critical value. The states of the system that possess good angular momentum quantum numbers are scrutinized and connections between the angular momentum and the fragmentation of the states are investigated. In two spatial dimensions mean-field states can describe states of good angular momentum. Using a mean-field ansatz, analytical results for the energy, the occupation numbers and the stability of the ground state carrying L quanta of angular momentum are obtained. In three dimensions, however, a mean-field theory does not suffice for the proper description of angular momentum states. The eigenstates of both total angular momentum operators (L^2 and L_z) are derived and it is shown that they are generally many-body states. It is shown, moreover, that angular momentum has a general stabilizing effect on the gas and this connection is expressed quantitatively. Finally, the ground state of the gas is examined, when its container is set into external rotation. It is found that due to the attraction the symmetry of the ground state does not change, angular momentum is not transfered from the rotation to the gas and thus no significant impact in the stability is seen.