Abstract
Feshbach Resonance (a concept close to Fano resonance) is a central tool in manipulating interaction between atoms in a cold atom gas. It occurs when two interacting atoms can be found in two different channels that are coupled to each other: an open one and a closed one, in which they are bound. The energy difference between the potentials in the two channels is experimentally tunable. According to the paradigm, a Feshbach (zero-energy) resonance in the scattering of two atoms occurs if the binding energy in the closed channel is close to the (very low) scattering energy in the open channel. In that case, the scattering length is very large (ideally a=\pm \infty). Since the interaction between cold atoms is approximately proportional to the scattering length, we have the possibility to control the strength atom-atom interaction in real experiments.
Using a tight-binding model to describe the two atom system I derive a remarkably simple expression for the scattering phase shift from which all physical properties at low energy scattering can be easily elucidated. Three results that are unexpected are: 1) When there is a Feshbach resonance, the binding energy in the closed channel is always higher than the resonance energy (this is the Thomas-Ehrman shift known in Nuclear Physics). 2) The sign of the scattering length at resonance depends critically on the strength of coupling between the two channels. 3) For large enough coupling strength a zero energy (Feshbach) resonance is possible even when the closed channel potential is repulsive (hence it does not have a bound-state at all).
Coffee and tea will be served 20 minutes prior to the seminar.