In this talk, we will explain the effect of quantum interactions exchanging different types of particles. We will consider a system made of two fermions and one boson, in order to study the effect of such an off-diagonal interaction term. We will in particular show the existence of exponentially localized dressed bound fermion pairs. We will give particular attention to the regime of very large on-site (Hubbard) repulsions, because this situation is relevant for cuprate superconductors. Indeed, in the meantime, we will explain the high- temperature superconductivity of cuprates and apply our model to such physical systems.