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Journal of Atomic, Molecular, and Optical Physics
Volume 2012 (2012), Article ID 241051, 9 pages
Research Article

Effective Potential for Ultracold Atoms at the Zero Crossing of a Feshbach Resonance

1Department of Physics, Harvard University, Cambridge, MA 02138, USA
2Department of Physics and Astronomy, University of Aarhus, 8000 Aarhus, Denmark

Received 25 February 2012; Revised 25 June 2012; Accepted 26 June 2012

Academic Editor: Ali Hussain Reshak

Copyright © 2012 N. T. Zinner. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider finite-range effects when the scattering length goes to zero near a magnetically controlled Feshbach resonance. The traditional effective-range expansion is badly behaved at this point, and we therefore introduce an effective potential that reproduces the full T-matrix. To lowest order the effective potential goes as momentum squared times a factor that is well defined as the scattering length goes to zero. The potential turns out to be proportional to the background scattering length squared times the background effective range for the resonance. We proceed to estimate the applicability and relative importance of this potential for Bose-Einstein condensates and for two-component Fermi gases where the attractive nature of the effective potential can lead to collapse above a critical particle number or induce instability toward pairing and superfluidity. For broad Feshbach resonances the higher order effect is completely negligible. However, for narrow resonances in tightly confined samples signatures might be experimentally accessible. This could be relevant for suboptical wavelength microstructured traps at the interface of cold atoms and solid-state surfaces.