The attractive Bose gas in two dimensions: an analytical study of its fragmentation and collapse

Abstract

An attractive Bose-Einstein condensate in two spatial dimensions is expected to collapse for supercritical values of the interaction strength. Moreover, it is known that for nonzero quanta of angular momentum and infinitesimal attraction the gas prefers to fragment and distribute its angular momentum over different orbitals. In this work we examine the two-dimensional Bose gas for finite values of attraction and describe the ground state in connection to its angular momentum by theoretical methods that go beyond the standard Gross-Pitaevskii theory. By applying the best mean field approach, we derive analytical relations for the energy, the fragmentation of the ground states and the critical (for collapse) value of the attraction strength as a function of the total angular momentum $L$.