Feshbach Resonance in a Tight-Binding Model    [PDF]

Y. Avishai, Y. B. Band, M. Trippenbach
The physics of Feshbach resonance is analyzed using an analytic expression for the s-wave scattering phase-shift $\delta(\veps)$, where $\veps$ is the scattering energy, derived within a two-channel tight-binding model. It is found that $\delta(\veps)$ (hence the scattering length) changes sign when the coupling $t$ between the open and closed channel crosses a certain threshold value $t_0$. An explicit expression is obtained for the experimentally tunable energy difference between the open and closed channel asymptotic potentials at which resonance occurs. When the closed channel has a bound state, an expression is derived for the energy difference between the closed channel bound state energy $\veps_B$ and $\veps$ at resonance. Analysis of bound states and finite energy resonances of the coupled system is carried out in terms of the Jost function. Remarkably, for strong enough coupling $t$, a Feshbach resonance can exist even when the closed channel does {\em not} have a bound state. This could enrich the physics of BCS-BEC crossover and BEC dynamics.
View original: http://arxiv.org/abs/1306.0144