Two-channel Feshbach physics in a structured continuum
Abstract
We analyze the scattering and bound state physics of a pair of atoms in a one-dimensional optical lattice interacting via a narrow Feshbach resonance. The lattice provides a structured continuum allowing for the existence of bound dimer states both below and above the continuum bands, with pairs above the continuum stabilized by either repulsive interactions or their center-of-mass motion. Inside the band the Feshbach coupling to a closed channel bound state leads to a Fano resonance profile for the transmission, which may be mapped out by rf or photodissociative spectroscopy. We generalize the scattering length concept to the one-dimensional lattice, where a scattering length may be defined at both the lower and the upper continuum thresholds. As a function of the applied magnetic field the scattering length at either band edge exhibits the usual Feshbach divergence when a bound state enters or exits the continuum. Near the scattering length divergences the binding energy and wave function of the weakly bound dimer state acquires a universal form reminiscent of those of free-space Feshbach molecules. We give numerical examples of our analytic results for a specific Feshbach resonance, which has been studied experimentally.
- Publication:
-
Physical Review A
- Pub Date:
- August 2008
- DOI:
- 10.1103/PhysRevA.78.023617
- arXiv:
- arXiv:0802.3808
- Bibcode:
- 2008PhRvA..78b3617N
- Keywords:
-
- 03.75.Lm;
- 34.10.+x;
- 63.20.Pw;
- 71.23.An;
- Tunneling Josephson effect Bose-Einstein condensates in periodic potentials solitons vortices and topological excitations;
- General theories and models of atomic and molecular collisions and interactions;
- Localized modes;
- Theories and models;
- localized states;
- Condensed Matter - Other;
- Quantum Physics
- E-Print:
- 18 pages, 9 embedded figures