Tuning the scattering length by periodic modulation*

We consider a 3D interacting gas with a small time-periodic modulation of the attractive potential, which can be achieved by using a Feshbach resonance. The steady state is described by the Floquet formalism, which leads to a simple recurrence formula for an effective scattering length a_eff. For frequencies corresponding to the bound-state of the potential without driving, we observe strong resonances, which allow the tuning to very large positive and negative values of a_eff with relatively small imaginary parts.