Collapse and stable self-trapping for Bose-Einstein condensates with 1/rb-type attractive interatomic interaction potential
Abstract
We consider dynamics of Bose-Einstein condensates with long-range attractive interaction proportional to 1/rb and arbitrary angular dependence. It is shown exactly that collapse of a Bose-Einstein condensate without contact interactions is possible only for b⩾2. The case b=2 is critical and requires the number of particles to exceed a critical value to allow collapse. The critical collapse in that case is a strong one, trapping into the collapsing region a finite number of particles. The case b>2 is supercritical with an expected weak collapse which traps a rapidly decreasing number of particles during approach to collapse. For b<2 a singularity at r=0 is not strong enough to allow collapse but an attractive 1/rb interaction admits stable self-trapping (a stable three-dimensional soliton solution) even in the absence of an external trapping potential.
- Publication:
-
Physical Review A
- Pub Date:
- August 2010
- DOI:
- 10.1103/PhysRevA.82.023615
- arXiv:
- arXiv:1002.1469
- Bibcode:
- 2010PhRvA..82b3615L
- Keywords:
-
- 03.75.Kk;
- 03.75.Lm;
- Dynamic properties of condensates;
- collective and hydrodynamic excitations superfluid flow;
- Tunneling Josephson effect Bose-Einstein condensates in periodic potentials solitons vortices and topological excitations;
- Nonlinear Sciences - Pattern Formation and Solitons;
- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- Phys. Rev. A 82, 023615 (2010)