2005/09/05 by Michiel Wouters, M. Wouters, G. Orso +1 · 45 citations
Physics and Astronomy · #Advanced Chemical Physics Studies #Amplitude #Anisotropy #Bound state #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Crossover #Lattice (music) #Optical lattice #Periodic potential #Physics #Quantum mechanics #Quantum tunnelling #Scattering #Scattering length #Semiconductor Quantum Structures and Devices #Statistical physics #cond-mat.other
paper · pdf · doi:10.1103/physreva.73.012707
published in Physical Review A 73(1) (American Physical Society)
arxiv created 2005/09/05 · openalex publication_date 2006/01/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.