Self-binding transition in Bose condensates with laser-induced “gravitation”

In our recent publication [D. O'Dell et al., Phys. Rev. Lett. 84, 5687 (2000)] we proposed a scheme for electromagnetically generating a self-bound Bose-Einstein condensate with $1/r$ attractive interactions: the analog of a Bose star. Here we focus upon the conditions necessary to observe the transition from external trapping to self-binding. This transition becomes manifest in a sharp reduction of the condensate radius and its dependence on the laser intensity rather than the trap potential.