Two-body problem in periodic potentials
Other Condensed Matter
2009-11-11 v1
Abstract
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 . 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 . For the special case D=1, we also compare our analytical predictions with exact numerics, finding remarkably good agreement.
Cite
@article{arxiv.cond-mat/0509093,
title = {Two-body problem in periodic potentials},
author = {M. Wouters and G. Orso},
journal= {arXiv preprint arXiv:cond-mat/0509093},
year = {2009}
}