Alternative Route to Strong Interaction: Narrow Feshbach Resonance

We show that a narrow resonance produces strong interaction effects far beyond its width on the side of the resonance where the bound state has not been formed. This is due to a resonance structure of its phase shift, which shifts the phase of a large number of scattering states by $\pi$ before the bound state emerges. As a result, the magnitude of the interaction energy when approaching the resonance on the "upper" and "lower" branch from different side of the resonance is highly asymmetric, unlike their counter part in wide resonances. Measurements of these effects are experimentally feasible.