We describe two-field optical techniques to control interactions in Feshbachresonances for two-body scattering in ultra-cold gases. These techniques createa molecular dark state in the closed channel of a magnetically tunable Feshbachresonance, greatly suppressing optical scattering compared to single opticalfield methods. The dark-state method enables control of the effective range, bycreating narrow features that modify the energy dependence of the scatteringphase shift, as well as control of the elastic and inelastic parts of thezero-energy s-wave scattering amplitude. We determine the scattering length andthe effective range from an effective range expansion, by calculating themomentum-dependent scattering phase shift from the two-body scattering state.
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