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Title: Two-body problem in periodic potentials

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 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.

Authors:
 [1];  [2]
  1. BEC-INFM and Dipartimento di Fisica, Universita di Trento, 1-38050 Povo (Italy)
  2. TFVS, Universiteit Antwerpen, Universiteitsplein 1, 2610 Antwerpen (Belgium)
Publication Date:
OSTI Identifier:
20786711
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 73; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.73.012707; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ANISOTROPY; ATOM-ATOM COLLISIONS; ATOMS; BOUND STATE; COMPARATIVE EVALUATIONS; PERIODICITY; POTENTIALS; S WAVES; SCATTERING AMPLITUDES; SCATTERING LENGTHS; THREE-DIMENSIONAL CALCULATIONS; TUNNEL EFFECT; TWO-BODY PROBLEM

Citation Formats

Wouters, M, TFVS, Universiteit Antwerpen, Universiteitsplein 1, 2610 Antwerpen, and Orso, G. Two-body problem in periodic potentials. United States: N. p., 2006. Web. doi:10.1103/PHYSREVA.73.0.
Wouters, M, TFVS, Universiteit Antwerpen, Universiteitsplein 1, 2610 Antwerpen, & Orso, G. Two-body problem in periodic potentials. United States. https://doi.org/10.1103/PHYSREVA.73.0
Wouters, M, TFVS, Universiteit Antwerpen, Universiteitsplein 1, 2610 Antwerpen, and Orso, G. 2006. "Two-body problem in periodic potentials". United States. https://doi.org/10.1103/PHYSREVA.73.0.
@article{osti_20786711,
title = {Two-body problem in periodic potentials},
author = {Wouters, M and TFVS, Universiteit Antwerpen, Universiteitsplein 1, 2610 Antwerpen and Orso, G},
abstractNote = {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.},
doi = {10.1103/PHYSREVA.73.0},
url = {https://www.osti.gov/biblio/20786711}, journal = {Physical Review. A},
issn = {1050-2947},
number = 1,
volume = 73,
place = {United States},
year = {Sun Jan 15 00:00:00 EST 2006},
month = {Sun Jan 15 00:00:00 EST 2006}
}