The Fano effect [U. Fano, Phys. Rev. 124, 1866 (1961)] shows that an inelastic scattering process can be suppressed when the output channel (OC) is coupled to an isolated bound state. The Fano effect was originally derived via a first-order perturbation treatment for coupling between the incident channel (IC) and the OC. In this paper, we first generalize the Fano effect to systems with arbitrarily strong IC-OC couplings. We analytically prove that, in a system with one IC and one OC, when the interatomic interaction potentials are real functions of the interatomic distance, the exact s-wave inelastic scattering amplitude can always be suppressed to zero by coupling between the IC or the OC (or both of them) and an extra isolated bound state. We further investigate the application of this generalized Fano effect for the suppression of two-body collisional losses of ultracold atoms and show that when the low-energy inelastic collision between two ultracold atoms is suppressed by this effect, the real part of the elastic scattering length between the atoms is still capable of being much larger than the range of interatomic interaction. In addition, when open scattering channels are coupled to two bound states, with the help of the Fano effect, independent control of the elastic and inelastic scattering amplitudes of two ultracold atoms can be achieved. Possible experimental realizations of our scheme are also discussed.
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