Two-body problem in periodic potentials
- BEC-INFM and Dipartimento di Fisica, Universita di Trento, 1-38050 Povo (Italy)
- TFVS, Universiteit Antwerpen, Universiteitsplein 1, 2610 Antwerpen (Belgium)
We investigate the problem of two atoms interacting via a short range s-wave potential in the presence of a deep optical lattice of arbitrary dimension D. Using a tight-binding approach, we derive analytical results for the properties of the bound state and the scattering amplitude. We show that the tunneling through the barriers induces a dimensional crossover from a confined regime at high energy to an anisotropic three-dimensional regime at low energy. The critical value of the scattering length needed to form a two-body bound state shows a logaritmic dependence on the tunneling rate for D=1 and a power law for D>1. For the special case D=1, we also compare our analytical predictions with exact numerics, finding remarkably good agreement.
- OSTI ID:
- 20786711
- Journal Information:
- Physical Review. A, Vol. 73, Issue 1; Other Information: DOI: 10.1103/PhysRevA.73.012707; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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