Linewidth prevents macroscopic quantum superposition generation by single atom dispersion

A method for generating macroscopically distinguishable superposition states via single atom dispersion was proposed by Savage et al. see Optics Letters, vol.15, p.628, 1990. In that model, the atomic linewidth was not considered. However, including the atomic linewidth, the authors get two contradictory conditions for the generation of distinguishable superposition states. This shows that the atomic linewidth prevents the formation of macroscopically distinguishable superposition states by the proposed method.