Feshbach Resonance in a Tight-Binding Model

Abstract

The physics of Feshbach resonance is analyzed using an analytic expression for the $s$-wave scattering phase-shift and the scattering length $a$ which we derive within a two-channel tight-binding model. Employing a unified treatment of bound states and resonances in terms of the Jost function, it is shown that for strong inter-channel coupling, Feshbach resonance can occur even when the closed channel does not have a bound state. This may extend the range of ultra-cold atomic systems that can be manipulated by Feshbach resonance. The dependence of the sign of $a$ on the coupling strength in the unitary limit is elucidated. As a by-product, analytic expressions are derived for the background scattering length, the external magnetic field at which resonance occurs, and the energy shift $\epsilon -{\epsilon }_B$, where $\epsilon$ is the scattering energy and ${\epsilon }_B$ is the bound state energy in the closed channel (when there is one).

5 pages with 1 figures + 6 supplementary material pages with 4 figures. Substantial changes compared with previous version

References in corpus (3)

• Two-particle states in the Hubbard model
• Systematic study of Optical Feshbach Resonances in an ideal gas
• Feshbach Molecules in a One-dimensional Optical Lattice

Cited by in corpus (3)

• Resonant pair-exchange scattering and BCS-BEC crossover in a system composed of dispersive and heavy incipient bands: a Feshbach analogy
• Orbital Feshbach Resonance with Small Energy Gap between Open and Closed Channels
• Simple model of Feshbach resonance in the strong-coupling regime